DAMASCUS, Syria - Former U.S. President Jimmy Carter pressed ahead with his personal Mideast peace mission Friday, arriving in Syria where he planned to meet the exiled leader of Hamas.

In Israel, Cabinet minister Eli Yishai said he asked Carter to tell Hamas he wants to meet with the Palestinian militant group to discuss a prisoner exchange. The Israeli government has long refused to deal with Hamas, which is sworn to the Jewish state's destruction.

Carter planned to meet Hamas chief Khaled Mashaal Friday in Damascus, where Mashaal lives in exile. He will also have talks with Syrian President Bashar Assad.

The former American president already met Hamas representatives twice this week, brushing aside criticism from Israel and the U.S. government. In Cairo Thursday, Carter asked senior Hamas officials from Gaza to halt rocket attacks against Israel. And in the West Bank Wednesday, he embraced a Hamas representative, angering Israelis.

The U.S. government has distanced itself from Carter's contacts with Hamas, saying it is purely a personal initiative. The U.S. and Israel consider Hamas a terrorist organization.

But Carter defended his mission on Thursday.

"You can't have an agreement that must involve certain parties, unless you talk to those parties to conclude the agreement," he said in a speech at the American University in Cairo. "You have to involve Hamas ... They have to be involved in some way."

Carter also said Thursday he knows some Israeli government officials are "quite willing" to meet Hamas and speculated that might happen in the near future.

Yishai, the Israeli deputy prime minister, said Friday he asked Carter to arrange a meeting with Hamas to try to win the release of captured Israeli soldier Gilad Shalit, held by Hamas in Gaza for two years.

Hamas said Friday Shalit will "not see the light" until Palestinian prisoners are also released in an exchange.

Yishai was the only Israeli minister to meet Carter when he visited Israel and the Palestinians territories earlier this week. He said Friday if he does meet with Hamas, he would not discuss Israel-Gaza fighting so as not to violate the government ban on negotiating with the militants.

Israeli Prime Minister Ehud Olmert said he did not meet Carter during his visit to avoid creating the impression that he was negotiating with Hamas.

Moussa Abu Marzouk, deputy head of Hamas' Syria-based political bureau, told The Associated Press that calming the situation between Hamas and Israel as well as the fate of Shalit would on the agenda in Carter's meeting with Mashaal.

"Hamas will not be a hurdle in any future prisoner exchange," Abu Marzouk said.

Asked if Hamas is ready to sit and talk directly to the Israelis, Abu Marzouk said: "There are no (direct) meetings with the Israelis. Most of the meetings that took place between the two sides were not direct."

Hamas won 2006 Palestinian parliament elections and 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.

But an internationally backed Israeli boycott of Hamas has put a stranglehold on Gaza, deepening the poverty of its 1.4 million residents.

Hamas officials have said the meetings with Carter have given the group legitimacy.

Hamas official Mushir Masri, in a fiery speech Friday to thousands of Hamas supporters in Gaza, said the meetings with Carter were proof that Hamas was not a terrorist group, but a national liberation movement.

He said countries and groups are beginning to understand that Hamas is a power to reckon with and the region will not have calm or stability without engaging the group.

"It confirms the failure of the U.S. and European policies of ignoring Hamas," he told the crowd. "It confirms that all the countries that assume Hamas is a terrorist group should reconsider."

----

Associated Press reporter Diaa Hadid contributed to this report from Gaza.