Echoing criticism from US 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 having 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 US 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 his deputy, Moussa Abu Marzouk, making it illegal to conduct any transactions with them. Marzouk, who attended Friday's meeting 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. Daniel Kurtzer, a former US ambassador to Israel under President Bush, called Carter's meetings with Hamas officials "a strategic and tactical mistake." "Palestinians believe they cannot implement a peace agreement without Hamas, but they also understand that they can't reach such an agreement with Hamas in power," Kurtzer said. Martin Indyk, a US ambassador to Israel under President Clinton, said "the problem with trying to bring Hamas into the negotiations is it will force Israel out." Israel brands Hamas a terrorist organization and has accused Mashaal of masterminding the kidnapping of Schalit 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. Deputy Prime Minister Yishai, was the only minister to meet Carter when he visited Israel earlier this week. Prime Minister Ehud Olmert said he did not meet Carter during his visit to avoid creating the impression that he was negotiating with Hamas. Carter met senior Hamas officials from Gaza in Cairo on Thursday and asked them to halt rocket attacks against Israel. In the West Bank on Wednesday, he embraced a Hamas representative. Though the government refuses to deal with Hamas, Carter said Thursday he knows some Israeli government officials are "quite willing" to meet the militant group. Yishai said Friday he asked Carter this week to arrange a meeting with Hamas to discuss a prisoner exchange. He said he wanted to try to win the release of Schalit. 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.