Former US president Jimmy Carter's talks with Hamas leaders constitute de facto recognition of the Islamic movement's legitimacy, a senior Hamas official in the Gaza Strip said on Sunday. Carter met with Hamas chief Khaled Mashaal over the weekend in Damascus, where he also held discussions with Syrian President Bashar Assad. After meeting with Jordan's King Abdullah on Sunday, the former US president was scheduled for a return trip to Israel on Monday. "Carter's visit to the region and his meetings with Hamas leaders are seen as recognition of the fact that Hamas is a major player that can't be ignored," said Ismail al-Ashkar, a top representative of Hamas. "The meetings show that there is no denying the fact that Hamas won the [January 25, 2006,] parliamentary election and should be part of any process." Noting that Carter had personally supervised that election, Ashkar said Hamas welcomed Carter's visit because he would be able to convey to the world the "real picture of the Palestinian suffering." Hamas, Ashkar added, wanted its message to reach the entire world. "Carter is a widely-respected international figure whose voice is heard by many," he said. "In any case, we want the world to understand that the resistance is the only way to restore the rights of the Palestinians, and that's why we are launching attacks deep inside Israel." Carter's talks with Mashaal and other Hamas leaders in Cairo and Damascus focused on kidnapped IDF soldier Cpl. Gilad Schalit and ways of reaching a truce with Israel, Ashkar said. He said the Hamas leaders told Carter that they were eager to resolve the Schalit case and end the blockade on Gaza. "Our position remains that Israel must free Palestinian prisoners in return for Schalit," he said. "We also want an end to the unjust siege imposed on our people in the Gaza Strip." On Sunday, Al-Jazeera reported that Hamas had rejected a new Egyptian cease-fire proposal between it and Israel. Meanwhile, Hamas leaders hailed Saturday morning's attack on the Kerem Shalom crossing between the southern Gaza Strip and Israel as a "heroic" operation. They said similar attacks would be carried out in the coming days until Israel was forced to lift the blockade. "This operation is a severe blow to Israel's security concept," Hamas spokesman Fawzi Barhoum said. "The Zionist enemy has been hit in the most sensitive area. This is the area used by the Zionists to send their attacks and troops into the Gaza Strip." Barhoum said the attack followed threats by Hamas that it would not remain idle in the face of the continued blockade. "We have said that the Zionists would bear responsibility for the ongoing siege," he said. "Hamas has carried out its promise to end the siege." Syrian president Assad, who met with Carter on Friday to discuss prospects for renewed peace negotiations with Israel, reportedly announced Sunday that he has exchanged messages with Israel through a third party to explore the possibility of resuming talks with Jerusalem, the country's official news agency SANA reported. During a meeting with ruling Ba'ath Party officials, Assad commented on media reports about indirect contact between the two countries. "There are efforts exerted in this direction," he was quoted as saying. Yediot Aharonot on Thursday quoted Prime Minister Ehud Olmert as saying Israel and Syria had been exchanging messages to clarify expectations for any future peace treaty. He didn't disclose the content of the messages or provide other details about the contacts. The paper quoted Olmert as saying, "They know what we want from them, and I know full well what they want from us." Assad echoed those comments on Sunday, saying Israel "knows well what is accepted and not accepted by Syria." "Syria rejects secret [direct] talks or contacts with Israel... Anything Syria does in this regard will be announced to the public," Assad was quoted as saying.