Syria presumably has handed over all the Iraqi leaders known to have fled to Damascus and other areas of the country during Operation Iraqi Freedom, Secretary of State Colin Powell (search) said Sunday.

In an interview with CBS on Sunday, Powell said "some have been made available to us, let me put it that way, who we knew were there, are no longer there.

"They've been made available to us, and they will be before the bar of justice of the Iraqi people. There are other names that we have passed back and forth to see whether they can be located."

Powell said that during his three-hour meeting with Syrian President Bashar Assad (search) in Damascus (search) on Saturday, the foreign leader seems to have "no interest in serving as a haven for any of these individuals."

"So I think if we can give him information and give him specific names and anything else we can say about these people, I think he would try to respond."

The Bush administration has charged that Syria has been providing safe haven to Iraqi regime leaders looking to escape the coalition's hunt for Saddam Hussein's inner circle. Syria has vehemently denied the charges.

Powell said there may be other Iraqi figures in Syria that the United States does not know about. He told Assad that Washington expects those people too to be handed over.

"If you really want to have a more positive relationship with us and with your new neighbors in Iraq, this is the time for you to locate these individuals and turn them over to Iraqi justice and not allow Syria to become a haven for materials that might be coming out of Iraq still, or came out of Iraq, or individuals who are trying to seek haven," Powell said he told Assad.

There have been numerous reports that Syria has supplied various supplies, such as night-vision goggles and possible weapons, to Iraq. The Pentagon also says Syria has been producing chemical weapons.

But Assad said Saturday that no weapons of mass destruction were transferred to Syria by the Iraqis, Powell said.

The Bush administration has consistently suggested that Saddam moved and hid weapons in Syria.

"They say that they have taken in no weapons of mass destruction from Iraq," Powell said. "Their position is that they think it unlikely that Saddam Hussein would have trusted them with such weapons."

Powell told NBC's Meet the Press Sunday that the Bush administration and Congress are closely monitoring Syria's moves.

"There are no illusions in his mind as to what we are looking for from Syria," Powell said. "We will see what happens in the days, weeks, months ahead."

Some U.S. lawmakers favor legislation imposing economic penalties against Syria if Damascus does not make changes. The Syria Accountability Act, for example, "will hurt them ... in the absence of performance on their part," Powell said.

Powell laid out a strict set of guidelines to Assad he believes Syria must respect in order to survive alongside an Iraq no longer ruled by Saddam.

Powell told ABC's This Week that if Syria keeps its eastern border closed, tracks down and surrenders any Iraqi suspects and cooperates with rebuilding Iraq -- including the formation of a democratic government, "then that tells us one thing about Syria's decision to move forward: that they looking for a better relationship with United States. If they do not, then there will be consequences."

Syria's oil from Iraq and other trade going both ways have been shut off, Powell added.

The Powell-Assad discussion also included talks about Syria's support for the Lebanese militant group Hezbollah.

Powell said Syria indicated it had closed certain Palestinian offices in Damascus; Powell had been expected to bring up the offices kept in Syria by groups such as the militant Hamas and Islamic Jihad, which the Bush administration classifies as terrorist organizations.

"We provided some other suggestions to the Syrians that they are going to take in advisement. I expect to hear back," Powell said.

A senior State Department official said Powell told Assad that the United States could not understand why those groups were seen "as of any benefit to Syria any longer" since Saddam's fall.

Powell said Sunday he told Assad that his support of terrorist groups, including harboring Palestinian organizations engaged in terror attacks against Israelis, "makes it hard to move forward on the Middle East peace process. These things have to come to an end."

In the meeting, Powell specifically mentioned Hamas, the Palestinian Islamic Jihad and the Popular Front for the Liberation of Palestine, General Command. The official said Powell noted that the United States would take the office closures as a sign of whether Syria really wants a new relationship with the United States "on a new foundation, not just some incrementalism from the past."

Militant Palestinian groups said Powell's comments won't affect the resistance against Israel.

"This is not going to affect the Palestinian resistance," said Hamas spokesman Mahmoud Zahar. "Hamas has a symbolic presence in Syria. The resistance is here inside the occupied land and it is going to continue."

The Islamic Jihad leader in Gaza, Dr. Mahammed Hindi, said the United States has called for this several times before and said his group doesn't have offices in Damascus. "Our movement is inside Palestine and we will continue our work from inside Palestine," he said.

Ziad Naghalah, a member of Islamic Jihad's politbureau in Damascus, said: "We have not been notified about the closure of our offices. Our offices in Syria are information offices."

"There is nothing in Hezbollah's dictionary called 'withdrawal' because this will amount to the abolishment of [Hezbollah's] presence and even the cancellation of Lebanon from the current political map," said Hussein Khalil, a political assistant to Hezbollah leader Sheik Hassan Nasrallah.

Powell said he made clear that the U.S. commitment to Middle East peace "would include Syria and Lebanon, and would include the Golan Heights," a particularly sensitive issue for Syria. The Golan Heights are a rocky frontier plateau held by Israel since the 1967 Middle East War.

After the meeting with Assad, Powell left for Beirut to try to sell Lebanon on the U.S.-sponsored "road map" for peace between Israel and the Palestinians.

There, Powell assured Prime Minister Rafik Hariri of U.S. support for "an independent and prosperous Lebanon free of all -- all -- foreign forces." As he did with Syria, he emphasized the Israeli-Palestinian "road map" is envisioned as the path to a settlement that also includes the interests of Syria and Lebanon.

"We are interested in a comprehensive solution that will involve creation of a Palestinian state and settling the outstanding issues between Israel and Lebanon, and Israel and Syria," Powell said.

The secretary will return to the region next week to see Israeli Prime Minister Ariel Sharon and Mahmoud Abbas, the new Palestinian prime minister.

Fox News' Teri Schultz and The Associated Press contributed to this report.