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Stopping the Israeli assault on Hezbollah targets in Lebanon would end the immediate armed conflict but won't address the root cause of the problems in the Mideast, President Bush told FOX News on Monday.

"It's a terrible situation where innocent people lose their lives. And yesterday's situation was awful," Bush told FOX News' Neil Cavuto, referring to the Israeli assault on Qana, Lebanon that ended in nearly 60 civilian deaths.

"I understand that, but it's also awful that a million Israelis are worried about rockets being fired from their — from their neighbor to the north. ... Israel's a sovereign nation, and she would defend herself. What we've got to do is put pressure on the world to help create the conditions so that when there's a cease-fire, it lasts. Stopping for the sake of stopping is — can be OK, except it won't address the root cause of the problem,“ Bush said.

Speaking to business leaders and Coast Guard members in the Port of Miami earlier Monday, Bush said he expects a U.N. resolution allowing a cease-fire in the Middle East to pass this week, and laid out short- and long-term changes that need to occur in the Middle East for sustainable peace and democracy to thrive there.

"We are going to work with our allies to bring before the United Nations Security Council a resolution that will end the violence and lay the groundwork for lasting peace in the Middle East," Bush said.

Bush said the immediate problem should be solved by Hezbollah ending its attacks on Israel, the return of Israeli soldiers taken hostage by terrorists, suspension of Israel's operations in Lebanon and eventual withdrawal of its troops.

Click here to read more about the Middle East conflict.

The president said for a longer term peace to prevail, Lebanon's government must be in power without the threat of disruptive forces to "exercise sole authority over its territory," a multi-national force must be dispatched to southern Lebanon along with humanitarian aid, Syria must "end its support for terror and respect the sovereignty of Lebanon" and Iran must end its "financial support and supply" for Hezbollah terrorists.

"For decades, the status quo in the Middle East permitted tyranny and terror to thrive. As we saw Sept. 11, the status quo in the Middle East led to death and destruction in the United States and it had to change. So America is opposing the forces of terror and promoting the causes of democracy across the greater Middle East," he said.

"This task is long, it is difficult work, but it is necessary work," Bush added.

In the interview with Cavuto, Bush said he thinks Iran is probably using the Mideast issue to deflect its own woes over demands that it suspend its uranium enrichment program. The United Nations passed a resolution on Monday giving Tehran 31 days to stop the program or face economic and diplomatic sanctions.

"I think that they sponsor Hezbollah, and therefore, I wouldn't be surprised if they're very much involved in the activities of Hezbollah. You know, this is a clash of governing styles. As these young democracies grow, you see terrorist groups trying to stop their advance. That's what happening in Iraq, that's what is happening in the Palestinian territories," Bush said.

Earlier, Bush said the United States will work with the United Nations to address "the root causes" of the conflict in the Middle East.

"We want there to be a long-lasting peace, one that is sustainable," he told Cuban-American business leaders at a breakfast held in a Cuban-style restaurant. "I assured the people here that we will work toward a plan at the United Nations Security Council that addresses the root causes of the problem, so that whatever comes out of the Security Council will be able to last and that the people of Lebanon and Israel will be able to remain in peace. That's what we want."

Bush returned to Washington, D.C., in the afternoon, where he will meet with Secretary of State Condoleezza Rice, who is on her way back from Israel.

"Condi is going to come back tonight and brief me about what she's -- what she heard, some of her conversations. And we will work with our allies on the Security Council to put a resolution forward that hopefully will work but will work in a system for sustainable peace," Bush told FOX News.

Speaking to reporters aboard the flight home, Rice said that she is "going to push very hard" for the Security Council resolution to be completed this week.

"I think it's time," she said. "I would hope that we're now going to actually do the work to put in place the conditions for a cease-fire."

Rice left Israel early after cutting short efforts at shuttle diplomacy between Jerusalem and Beirut following the Sunday bombing in Qana, a Lebanese town that Israel had cited as a hotbed of Hezbollah terrorists. The bomb hit a building that killed mostly women and children.

Israel then said it would halt aerial strikes for 48 hours to determine whether the targeting was correct in Qana. Early Monday local time, Israeli warplanes carried out airstrikes in southern Lebanon, near the village of Taibe. Israeli military officials said the actions only protected the ground forces operating in the area. The Israelis told U.S. officials that ground operations were continuing, and Monday's renewed air strikes were close-in support for operations against rocket launchers that were about to be used, said a U.S. official, speaking on condition of anonymity.

Israel had said when it agreed to suspend aerial operations that it was maintaining its right to respond to threats of attack being prepared against it, the official said, saying no authorization had been given to speak publicly on this subject.

The official added that it's important that the aerial suspension be implemented to allow humanitarian aid to be delivered and safe passage to continue.

Rice said she knew when she heard of the attack on Qana that her shuttle diplomacy would come to an end, but she did not think it was a deliberate attempt to end diplomatic efforts.

"The tragic incident happened in the midst of military operations. And, yes, it made things more difficult. But it was not that anyone intended to make things more difficult," she said, adding that U.S. officials will continue to consult with the Lebanese government.

After Sunday's hit on Qana, Lebanese Prime Minister Fuad Saniora said the talk of a larger peace package must wait until the firing stops. British Prime Minister Tony Blair, who spoke on the phone with Bush on Sunday, said Washington must work faster to put together the broader deal it seeks. "We have to speed this whole process up," Blair said. "This has got to stop on both sides."

Following the bombing, the U.N. Security Council met in emergency session and passed a statement expressing "extreme shock and distress" over Israel's bombing of civilians. U.N. Secretary-General Kofi Annan sharply criticized world leaders — implicitly Washington — for ignoring his previous calls for an immediate cease-fire.

As Bush spoke Monday, Russian and French officials criticized the U.S. refusal to accept an immediate cease-fire and promoted Iran as a force for stability in the region.

U.S. Ambassador to the United Nations John Bolton was bringing up a cease-fire resolution for Israel and Hezbollah at a Security Council meeting Monday on Iran's nuclear program. U.S. officials say they expect Saniora to support the resolution despite the fact he has said he's not willing to talk about a broader peace plan until Israel ends or suspends its military campaign.

Later in the day, the United Nations will also hold an informal meeting on a multi-national force for southern Lebanon. White House officials deny the Qana bombing has sped up the pace of diplomacy or shortening the time Israel has to weaken the terrorist group.

Undersecretary of State for Political Affairs Nicholas Burns told FOX News on Monday that the introduction of an international military force to police southern Lebanon would "prevent Hezbollah from lobbing those thousands of rockets that it has fired at Israel over the last two and a half weeks. So that's a very important part of bringing a permanent peace to that area."

Israeli officials seemed skeptical that Hezbollah would stop its attacks, which began July 12 with the kidnapping of two soldiers, and continued with the launching of thousands of Katyusha rockets at Israeli towns in the north. In response, Israel launched air raids and ground forces into the southern part of its neighbor to flush out the terrorists.

Israel's defense minister, Amir Peretz, told parliament that Israel would "expand and strengthen" its attack on Hezbollah. "It's forbidden to agree to an immediate cease-fire," Peretz said.

Burns said Israel wants some guarantees that if it agrees to a cease-fire, Hezbollah terrorists will also cease its attacks.

"That's why the sequencing of a cease-fire with this introduction of a military force is so important," Burns said.

Back in Miami, Bush said that observers must remember that "this crisis began with Hezbollah's unprovoked terrorist attacks against Israel. Israel is exercising its right to defend itself. And we mourn the loss of innocent life, both in Lebanon and in Israel."

FOX News' Wendell Goler and The Associated Press contributed to this report.