This is a rush transcript from "Special Report with Bret Baier," September 24, 2019. This copy may not be in its final form and may be updated.

BRET BAIER, ANCHOR: In the run-up to this week's United Nations session, perhaps the biggest question was would President Trump meet with Iranian President Hassan Rouhani to talk about the increasing hostilities between those two nations? So far, it has not happened. Not likely to happen.

Earlier today, President Trump called on allies to intensify pressure on Iran, as you just saw. Tonight, Fox News Sunday anchor Chris Wallace talks exclusively to the Iranian leader.


CHRIS WALLACE, FOX NEWS ANCHOR: Mr. President, you heard President Trump's speech today. He said no nation should support Iran's and "bloodlust and fanatical quest for nuclear weapons." Your response?

HASSAN ROUHANI, IRANIAN PRESIDENT (THROUGH TRANSLATOR): I am amazed at the interpretations of Mr. Trump vis-a-vis terrorism. Those who succeeded in Syria and in Iraq to bring terrorism to an end, eradicate Daish, ISIS. With the help of the Iraqi people and the Syrian people that was Iran. That was the country of Iran and the country that is present and flying over that airspace of and bombarding the soil of the country of Syria without permission of the government is the United States of America.

And today, America, unfortunately, is the supporter of terrorism in our region. And wherever America has gone, terrorism has expanded in their wake. Wherever we have gone on the other side, we have defeated terrorism.

One example is Daish or ISIS in our region. Vis-a-vis, the nuclear issue, we are committed to the Non-Proliferation Treaty as well as the protocols, the additional protocol. So, our activities are peaceful. Those who are going outside of the framework of the NPT is the United States of America. That is against the framework of the NPT conducting nuclear weapon tests.

WALLACE: We will get into your contention that is the U.S., not Iran. That is the sponsor of terror in a moment. But President Trump has spoken often about being willing to meet with you, even sometimes without preconditions. What do you think are the chances that this week at the United Nations, either in a formal setting or perhaps as they happen, these diplomatic sessions where you just happened to bump into each other, that you and President Trump will speak to each other?

ROUHANI: Why would we bump into one another? If we seek to pursue higher goals to benefit both countries, both people. It must be planned, and talks must be based on those plans. But prior to that, we must create mutual trust. And the trust is something that Mr. Trump took away from this framework. We had an agreement. Mr. Trump exited it without a valid justification, any legally from any international agreement. So, if the United States of America's government is willing to talk, it must create the needed conditions.

WALLACE: But it is no longer just President Trump, because this week the European countries who signed on to the Iran nuclear deal, I'm talking about Britain and France and Germany now say that they agree with President Trump that it was Iran that was responsible for the Saudi attack. The attack on Saudi oil facilities.

And like Mr. Trump, they say Iran should now agree to a bigger new deal on nuclear weapons and on regional stability and your missile systems. Will you agree to reopen the talks?

ROUHANI: Well, once we carried on negotiations with the United States of America for two years and during its 17-day period, the foreign minister of the Islamic Republic of Iran and the U.S. Secretary of State had continuous talks without returning to their countries. It was extremely difficult. But we did reach an agreement, which was signed, and it was enshrined in the United Nations Security Council resolution. And without a valid reason or cause, the United States left this agreement.

So, it took away the foundation of the needed trust. I think more than the issues it touched upon; the most basic needed issue is trust. And Mr. Trump damaged the trust between the two countries. So, this is very important. Trust must be restored and the restoration of trust consists in taking away the pressure imposed upon the nation and the people of Iran, which showed that clearly there is animosity even towards our children, our ill people, because we - they even have difficulty in obtaining basic medications and medical equipment.

This is a type of terrorism. This is inhumane. And if there is a cessation to this, then of course, the atmosphere will change of course. Of course, then it can be envisioned, then we can talk about many different topics of mutual interest for both sides, just as vis-a-vis the nuclear issue in the year 2015, we've reached an agreement. We can reach agreements on other topics as well.

WALLACE: But it seems for the last year and a half since the U.S. pulled out of the agreement, as if Iran's policy has been to drive a wedge between the U.S. President Trump and Europe, which has stood by the agreement. Now, this week, it seems, because of the fact that Iran was responsible for this attack on Saudi oil facilities, that you have, in fact, united the countries that has backfired on you. And now Europe has agreed with the U.S. that they need to reopen new talks.

ROUHANI: Well, first of all, vis-a-vis the oil installations in Saudi Arabia that were attacked that returns to the Saudi attack on the country of Yemen and the people of Yemen have the inherent right even brought in the United Nations charter to defend themselves. When they have been the subject of bombardments for over five years. Of course, the people of Yemen have the right to defend themselves and attack.

WALLACE: But Mr. President, the Saudis say the drones were not Yemeni. They were Iranian. They were delta wings and delta waves. The Saudis say, the cruise missiles were not Yemeni. They were Iranian. They were Ya Ali (ph) systems and even your closest partner in Europe, French President Macron seems to agree. He has agreed. He says that it is Iran that was responsible for the attack on Saudi Arabia.

ROUHANI: Well, because you are quite an experienced reporter. Mr. Wallace, you did not allow me to complete my previous answer. Not a problem. I will return to what you were speaking of. You see, Mr. Trump has leveled an accusation and unfounded accusation against Iran when the Saudi Arabian spokesperson announced that these - the equipment by which there were attacks were conducted were not Yemenis because on the weapons, they saw the name Ya Ali.

Well, there are Shiites in Yemen as well. So that spokesperson who thinks Iranians are all Shiites and Yemenis are not Shiites. They are mistaken. Ya All is chanting a slogan of aspiration that is chanted in Iraq, in Yemen, in Iran. So, quite frankly, it is really egregious for someone to say because of the word Ya Ali for them to attribute that to Iran.

But let's assume if it was from Iran, all of the moneys received from the United States for these defensive systems, for these weapons systems, radar systems installed in Saudi Arabia and throughout the Arabian Peninsula, how come they were not able to prevent that missile from hitting the target? So, what was the point of sending all of that Patriot anti-missile system? So that's quite frankly, even worse.

And if we accept the U.S. accusation, then it is even more embarrassing perhaps for the United States. And they must answer as to why they were not able to stop and intercept this system, the missile.

The Yemenis have quite advanced military capabilities. So, why is it that the intelligence agencies of the United States of America that are receiving large budgets from the taxpayer based in the United States? Why is it that they were completely unaware of these military Yemeni capabilities? So, they must be held to answer.

America must answer why did it sell the region so many systems, so many weapons? So, they must answer, why have they not been able to establish where it came from and then show the proof of it. Which radar system intercepted these weapons? Which one that put a lock - a radar lock on it as they were coming towards the target?

So, if this is all proven then they must answer why their defensive capabilities did not suffice? And why is it that America and the Europeans have been aiding the Saudi Arabians and their partners in conducting daily killings of the people of Yemen?

So, those who share in the bloodshed of the Yemeni people have no right to make such unfounded expressions. And last night in my meeting with Mr. Macron, I asked him, why do you say that Iran is responsible? He said, our technical experts have said that the Yemenis have not yet reached that type of technical capability, advanced technical capability. And in response, I told them that you are unaware of their capabilities.

So, if there is no ceasefire moving forward, you will see once again, and you will witness the military capabilities of the Yemenis. So, let's come together and find a solution. Leveling unfounded accusations are not constructive. Let's help the people of Yemen and not let them continue. Let's not let the Saudis continue the daily bombings. Peace is a much more attainable, beneficial place to go rather than attributing accusations at one another.

WALLACE: You talk about coming together and in fact, you are bringing to the UN a new peace plan called Hope, the Hormuz Peace Endeavor. But there are many nations in the region that say that Iran is the last country that should be proposing peace since they, they say you have mined tankers in the Persian Gulf. You have seized a British ship. You have shot down a United States drone. And now the Saudi oil attack, they say an Iranian peace plan is like putting the fox in-charge of a hen house.

ROUHANI: Iran during the past four decades has fought against terrorism unequivocally. And those who conducted killings inside Iran and martyred over 17,000 innocent civilians are now living their lives under your auspices here in the United States of America. And Mr. Bolton, who up until not too long ago was your National Security Adviser was on their payroll, giving speeches on their behalf. So, Iran is a country that has brought peace in the region.

WALLACE: Excuse me, sir. And I say this respectfully, you have given hundreds of millions, perhaps a billion dollars to Hezbollah, to Hamas, to various groups. That is not a supporter of terrorism?

ROUHANI: Well, you label people who fight for the defense of their country and their lands is terrorism. So, those who are the subjects of occupation, what should they do? Be passive and just look. You call the people in Yemen who are defending their country's terrorists and those who make the bombs and the missiles and the weapons systems and then make him readily available to the Saudi Arabians with which to target school buses, schools and weddings and hospitals? You do not find them guilty.

You say, why did you shoot down an American drone? But I ask you, why did you bring down a civilian airliner in which you killed over 290 civilian passengers? If we defended, we defended our territory, our country. But why is the United States present in our region? Why did the United States brought down a civilian airliner?

WALLACE: That's true. And it was a terrible, terrible act. And many years ago, but we're talking about Hamas, we're talking about Hezbollah, we're talking about firing missiles on the civilian areas. We're talking about blowing up people in civilian areas of the Israel. That's not terrorism?

ROUHANI: You defend an Israel, sir. The foundation of which is based upon attacking and surfing on the rights of others and on a daily basis has targeted the people of Palestine, Lebanon and most recently even Iraq as well as Syria. There is no terrorism throughout the world that matches the activities of Israel that has been seeking peace for the past 71 years, since its inception, since its founding.

So, those who fight for the freedom of their lands and their homes are not terrorists. Those are terrorists who render aid to Daish, to ISIS. Israel is the country that takes care of the injured ISIS fighters, and they make weapons available to them. So Daish, ISIS are the terrorist.

WALLACE: Israel supports ISIS?

ROUHANI: Certainly. Undoubtedly, do you have any doubts? Would you like to see the proof? You should visit Israeli hospitals and see the injured Daish, ISIS war fighters, how they're being taken care of. You should see the weapons captured from ISIS fighters and see that there are Israeli made.

The challenge is that sometimes American media outlets failed to reveal the truth to the American public. And they only receive the news from one specific viewpoint or channel, if you will. So that's why the people of America are quite frankly not very well aware of the realities in our region.

If the American people were to know that so many Yemenis on a daily basis with their money and their weapons systems are being innocently killed and their lives taken away, they would not stay silent.

WALLACE: Since President Trump pulled out of the nuclear deal last year, Iran has now taken steps to violate the agreement themselves. You have broken the limits on enriching uranium, on stockpiles of enriched uranium, and now you are using advanced centrifuges. If you were a year away from a nuclear weapon when you signed the Iran deal back in 2015, how much closer are you to a weapon today with these steps that you have taken.

ROUHANI: Well, the construct of your question, sir, is one that is based on prejudgment. First of all, the JCPOA, if we were seeking nuclear weapons, we would not have signed on to JCPOA. If we sought nuclear weapons, we would not have accepted the additional protocols.

WALLACE: But you agree that you have, but you agree that you have taken.

ROUHANI: Allow me to finish, please. Mr. Wallace, you are a veteran reporter. Allow me, but today, I don't understand why in the middle of my responses you are not giving me - you are not allowing me to complete my responses. Allow me to clarify one thing for everyone. Allow me to clarify what we are saying.

No country in the world accept that the nonproliferation treaty and the additional protocols, and for someone to accuse them of seeking nuclear weapons. If someone seeks nuclear weapons, why would they go under the controls of the IAEA? So this is not correct. We are not seeking nuclear weapons.

The country that have killed Japanese people with nuclear weapons and today has left the agreement previously signed with Russia for medium-range missiles and nuclear missiles and against the NPT is today building nuclear arsenals, today that country is America. Iran has lived up to her commitments and according to those commitments, we see that the ones who have broken the commitment is the United States of America, not Iran.

WALLACE: Have you made a calculation to wait until after the 2020 election and to negotiate, to wait and see if President Trump is defeated? Do you believe that perhaps Mr. Biden or another Democratic president would be easier to negotiate with?

ROUHANI: For us, it doesn't matter whether the United States president is a Democrat or a Republican. This is the purview and the prerogative of the United States of America and her people, of every American, whom they wish to choose.

We say that America should live up to her commitments, be it a Democrat or Republican president, a national commitment, the commitment of a country's, not based on a party in control of the presidency, of the executive branch.

So it was the country, the nation that gave the commitment.

So we want to see someone who will live up to these commitments, takes these commitments seriously. And it is us, the Islamic Republic of Iran, whom come today, as you mentioned earlier in one of your questions, we have given the hope initiative for peace, meaning the Hormuz Peace Initiative, the Hormuz Peace Endeavor. Therefore, we seek peace. That is why we have invited all countries in the region to come together so that we can reach peace and not allow the flames of war to continue to be fanned.

What makes the difference and is important for us is living up to one's international commitments. The commitment is something that was given by the government of the United States of America, so it really doesn't matter for us, our counterparts, which political party they come from.

WALLACE: Mr. President, thank you so much for speaking with us.

ROUHANI: Thank you.


BAIER: Chris Wallace with the Iranian president today.

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