DAMASCUS, Syria (AP) – Former U.S. President Carter defied U.S. and Israeli warnings and met twice this weekend with the exiled leader of Hamas and his deputy, two men the U.S. government has labeled terrorists and Israel accuses of masterminding attacks that have killed hundreds of civilians.

Carter is the most prominent American to hold talks with Khaled Mashaal, whose Palestinian militant group claimed new legitimacy from the meeting along with two other sessions the Nobel laureate held with Hamas leaders in the Middle East this week.

“Political isolation (of Hamas) by the American administration has begun to crumble,” Mohammed Nazzal, a top figure in Hamas’ political bureau, told The Associated Press after Friday’s meeting at Mashaal’s Damascus office.

Carter met Mashaal and his deputy, Moussa Abu Marzouk, again for about an hour Saturday morning, after more than four hours of talks the night before. “Several subjects were discussed, including Israeli-Palestinian) crossing points, (captured Israeli soldier Gilad) Shalit, the siege on the Palestinians and a cease-fire between Hamas and Israel,” Abu Marzouk said Saturday.

Another senior Hamas official in Damascus, speaking on condition of anonymity because he was not authorized to represent the group publicly, described the meetings as “warm.”

But he said Carter did not receive a response to either of the two requests the former president made: that Hamas halt its rocket attacks against Israel, and agree to a meeting with Israeli Deputy Prime Minister Eli Yishai to discuss a prisoner exchange.

Nazzal said Gaza-based Hamas leaders would travel to Syria on Saturday to confer with Mashaal, and that Carter “will be informed of Hamas’ response in the coming days.”

But underscoring the impression that Carter did not win any concessions, Hamas said Friday that Shalit would “not see the light” until Palestinian prisoners are also released in an exchange.

Carter’s convoy arrived at Mashaal’s office for the meeting under tight security, and reporters were prevented from getting near the site. The meetings were closed to media, and Carter was not available for comment. He left Damascus mid-morning Saturday, flying to Saudi Arabia for the next leg of his Mideast tour.

But Carter, who brokered the 1978 Israeli-Egyptian peace and was awarded the Nobel Peace Prize in 2002, has defended what he calls his personal peace mission. He says Hamas, which controls the Gaza Strip, must be engaged in order to achieve peace between Israel and the Palestinians.

The controversy over his visit highlights two different approaches to foreign policy. Some, like Carter, believe that is impossible to resolve a conflict without engaging all parties, even those responsible for attacks on civilians. Others, including the Bush administration, contend that such meetings give credibility to hard-line militants and allow them to play for time when they are not serious about peace. Echoing criticism from U.S. Secretary of State Condoleezza Rice before the trip, State Department spokesman Sean McCormack suggested Friday that Carter had opened himself up to “exploitation” by both Hamas and the Syrian government. “We find it very odd that one would encourage to have a conversation between the Israeli government and Hamas, which doesn’t even recognize the right of the Israeli government to exist,” McCormack said. “Is that really the basis of a conversation?”

Several members of Congress also urged Carter not to meet Hamas leaders, saying it would confer legitimacy on the group behind dozens of suicide bombings and other attacks that have killed some 250 Israelis.

“We have a policy in this country about Hamas. And he is just deliberately undermining that policy, and it’s wrong,” Rep. Sue Myrick, R-N.C., told Fox News on Friday, calling for the State Department to revoke the former president’s passport.

Friday’s meeting, which followed a session between Carter and Syrian President Bashar Assad, was the first public contact between a prominent American figure and Hamas officials since the Rev. Jesse Jackson met with Mashaal in Syria in 2006.

The U.S. government has no contact with Hamas after designating it a terrorist organization in 1995, an official label that means any financial or business transactions with the group are illegal. The government has also blacklisted Mashaal and Abu Marzouk, making it illegal to conduct any transactions with them.

Marzouk, who attended both meetings with Carter, has been accused of organizing a network of Islamic charities to funnel money to Hamas. He spent two years in prison in a New York jail after his name appeared on a list of people suspected of terrorist activity. He was deported in 1997.

Although long shunned by diplomats, Hamas thrust itself onto the international stage by winning the 2006 Palestinian parliament elections. It has since been locked in a power struggle with the Fatah faction headed by President Mahmoud Abbas. Hamas forcibly seized control of Gaza from Fatah in June and set up a regime that rivals Abbas’ West Bank government.

An internationally backed Israeli boycott of Hamas, partly an attempt to bolster Abbas’ faction, has put a stranglehold on Gaza, deepening the poverty of its 1.4 million residents.

After meeting earlier this week with Carter in Egypt, a top Hamas leader from Gaza said the militant group had resolved most of its differences with Fatah over security at the main Egypt-Gaza crossing, Rafah.

Mahmoud Zahar, one of the officials traveling Saturday to Damascus to confer with Mashaal, said Hamas had agreed to allow Fatah-allied guards at Rafah, something the group had previously opposed. His comments were carried Saturday by Egypt’s state-run MENA news agency.

Israel brands Hamas a terrorist organization and has accused Mashaal of masterminding the kidnapping of Shalit near Gaza two years ago. Israel has also blamed Mashaal and the group’s Damascus-based leadership of directing suicide bombings such as the September 2004 attacks that killed 16 Israelis in the southern city of Beersheba.

Israel tried to kill Mashaal in 1997, when agents sprayed him with poison on a street in Amman. Jordan’s late King Hussein, who had signed peace with Israel in 1994, forced Israel to send the antidote that saved his life. Afterward, Jordan expelled Mashaal to Qatar as the kingdom’s ties with Hamas deteriorated, and he moved to Damascus in 1999.