Former President Jimmy Carter met Friday with the exiled leader of Hamas and the militant group's deputy chief — on the 25th anniversary of the deadly bombing of the U.S. embassy in Beirut.

President Bush issued a statement Thursday calling on Americans to remember victims of the attack by a terrorist group known today as Hezbollah, which killed 17 Americans, 35 Lebanese citizens and wounded scores of others.

"On the 25th anniversary of that bombing, we mourn for those who perished, and we honor the sacrifice of their family and friends and of the many who were wounded," he said.

Bush also condemned "the regimes in Tehran and Damascus," which he said back Hezbollah and other terrorist groups. The U.S. State Department has designated Hamas a terrorist organization and refuses to negotiate with the group.

Carter's meeting with Hamas chief Khaled Meshal followed two other meetings between the former president and the Palestinian militant group in the Middle East this week. Hamas officials say the meetings have lent their group legitimacy.

Meshal's deputy Moussa Abu Marzouk attended the meeting with Carter at Meshal's Damascus office, a Hamas official at the site told The Associated Press. Abu Marzouk was designated a terrorist by the U.S. Treasury Department in 1995, allowing the government to seize his assets. He was detained at John F. Kennedy International Airport in New York that same year and spent two years in a New York jail before he was deported in 1997.

The U.S. State Department twice advised Carter against meeting Hamas leaders before he left on his Mideast trip earlier this week. More than 50 members of Congress also urged Carter not to meet Meshal, saying it would confer legitimacy on the group behind some 250 homicide bombings that have killed numerous Israelis.

But Carter, who brokered the 1978 Israeli-Egyptian peace and won the Nobel Peace Prize in 2002, has defended what he calls his personal peace mission, saying Hamas must be engaged in order to achieve Israeli-Palestinian peace.

Though Israel's government refuses to deal with Hamas, Carter said Thursday he knows some Israeli government officials are "quite willing" to meet the militant group and he speculated that might happen in the near future.

Israeli Cabinet minister Eli Yishai said Friday he asked Carter earlier this week to arrange a meeting with Hamas to discuss a prisoner exchange. Yishai, the Israeli deputy prime minister, said he wanted to try to win the release of Cpl. Gilad Shalit, held by Hamas in Gaza for two years.

Hamas said from Gaza Friday that 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. 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.

The U.S. State Department did not comment further on the meeting Friday.

"I don't think I have anything more to add to what I as well as others have said previously on it," State Department spokesman Sean McCormack told reporters. "We have made our views clear."

The United States designated Hamas a terrorist organization in January 1995, which made it a violation to conduct any financial or business transaction with the group.

Shortly after Hamas claimed responsibility for an August 19, 2003 suicide bombing in Jerusalem that killed 20 people including four U.S. citizens, the Treasury Department's Office of Foreign Asset Control named a number of Hamas leaders as "specially designated global terrorists." They included Meshal and Abu Marzouk and the designation made it illegal to conduct any transactions with them.

Israel also brands Hamas a terrorist organization and has accused Meshal of masterminding the kidnapping of Shalit near Gaza two years ago. Israel has blamed Mashaal and the group's Damascus-based leadership for 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.

Before Friday's meeting began, Abu Marzouk told The Associated Press that calming the situation between Hamas and Israel as well as the fate of Shalit would be on the agenda.

"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.

Carter met senior Hamas officials from Gaza in Cairo on Thursday and asked them to halt rocket attacks against Israel. And in the West Bank Wednesday, he embraced a Hamas representative, angering Israelis.

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.

"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."

Carter met Syrian President Bashar Assad earlier Friday after arriving in Syria from Egypt.

The Associated Press contributed to this report.