Former US president Jimmy Carter ended his nine-day trip to the region with a promise from Hamas to offer Israel tacit recognition and a 10-year truce if Israel in turn withdrew to the pre-1967 borders. Khaled Mashaal, whose group has sworn to destroy Israel, told reporters in Damascus on Monday that Hamas would accept a Palestinian state in the West Bank with Israel as its neighbor, but stressed that his group would not formally recognize it, a move immediately dismissed by the USas meaningless. "We agree to a (Palestinian) state on pre-67 borders, with Jerusalem as its capital with genuine sovereignty without settlements, but without recognizing Israel," Mashaal said."We have offered a truce if Israel withdraws to the 1967 borders, a truce of 10 years as a proof of recognition." Mashaal said he made the offer to Carter during talks between the two men on Friday and Saturday in the Syrian capital. Mashaal used the Arabic word "hudna," meaning truce, which is more concrete than "tahadiyeh" - a period of calm - which Hamas often uses to describe a simple cease-fire. Hudna implies a recognition of the other party's existence. In Washington, deputy State Department spokesman Tom Casey brushed aside Hamas's offer, saying the group's past rhetoric contained "all this language about truces and other kinds of issues. But the bottom line is, Hamas still believes in the destruction of the state of Israel; they don't believe Israel has a right to exist," adding it was clear "that nothing has changed" in Hamas's attitude - including that the group still refuses to explicitly recognize Israel and denounce terrorism. The statements by Hamas followed Carter's visit to the region, during which he spent time in Israel, Egypt, Jordan, Saudi Arabia and Syria. Carter angered both Israel and his own government by meeting with Hamas, which is considered by both countries to be a terrorist organization. It has carried out terror attacks in Israel, and has launched rockets against the country's southern border. It has also held Cpl. Gilad Schalit captive since June 2006. Top Israeli leaders, including Prime Minister Ehud Olmert, refused to meet with Carter during his stay. But Carter, who ended his visit to the region on Monday, said that it was critical to talk to Hamas. The former president, who brokered a peace deal between Egypt and Israel in 1979, said repeatedly that in those meetings, as well as in others he held, he was simply on a fact-finding mission for the Carter Center, which he runs in the United States. But he did more then just receive information. He tried and failed to broker deals regarding a cease-fire with Hamas and the release of Schalit. He did, however, wrangle a promise from Hamas that it would send a letter from the young man to his parents. The gesture was acknowledged by Mashaal on Monday, who told reporters in Damascus that he had agreed to this "humanitarian" gesture out of respect for Carter. Schalit's father, Noam, who, along with his wife, spoke with Carter both before and after his strip to Damascus, said he would wait until receiving the letter before commenting on the gesture. Speaking to the Israel Council on Foreign Relations, Carter said that Hamas had rejected his proposal for a rapid prisoner exchange that would allow Schalit to be moved to Egypt in exchange for the release of people held by Israel not guilty of violent crimes, including politicians, women and children. "Hamas considered its negotiations through Egypt to be well advanced," and it had already made promises to the families of prisoners who are on the prisoner list that is already under discussion with Israel, Carter said. But, he added, Hamas would be willing to move Schalit to Egypt after the first part of that deal brokered with Egypt had been concluded. Israel has agreed to release 1,000 prisoners in exchange for Schalit, but the hold-up has been the identity of the prisoners on the list. Ofer Dekel, the official charged by Olmert with dealing with the kidnapped soldiers issue, was reported as saying Monday that he had not received a briefing about Carter's activities in Damascus and his talks with Mashaal, government sources said. They added it was clear that Industry and Trade Minister Eli Yishai would brief the government - and Dekel - on what he heard from Carter regarding Schalit. The two men met both before and after Carter's talks with Mashaal. Far from knocking Carter's efforts, Yishai had asked Carter to help arrange a meeting between him and Hamas to work on releasing Schalit. Carter told Yishai that Hamas was interested in such a meeting, but did not want to talk to him at this time, out of fear it would complicate already existing negotiations. But Carter said he would help Yishai arrange a meeting in Egypt with intelligence chief Omar Sullieman. Yishai also spoke with Carter about his involvement in a conference of Islamic and Jewish religious leaders. But, while Yishai wanted to work with Carter, one government official said the former US president had done more harm than good, even with the promise of a new letter. The Schalit family had previously received a letter from their son last June. According to this official, Hamas is dissatisfied that, despite holding Schalit for almost two years, they have not gotten what they want from the Israeli government - the release of high-profile terrorists - for his return. In an attempt to pressure the Israeli public to pressure the government, Hamas is interested in opening up another negotiating track which bypasses Dekel and the government, and goes directly to the public. Carter, the official said, serves this purpose, because the impression that things could move much faster if only another channel of communications were tapped is exactly the message Hamas wanted the Israeli public to hear. The official said it was clear that Hamas was using Carter for its purposes, and that Mashaal, who knew far in advance that Carter was coming to Damascus to meet him, could very well have had a letter to give the former president from Schalit. It's all about shaping Israeli public opinion, the official said. The official said that Hamas also used Carter to give it legitimization. The US and European Union position is that Hamas should not be engaged until it accepts three preconditions: recognizing Israel, disavowing terrorism and accepting previous Israeli-Palestinian agreements. In comes Carter, the official said, and he meets Hamas without its having to pay any price, which is exactly what the organization wants to have happen with the rest of the world. But, during his Jerusalem speech, Carter defended his actions. "It was a small step forward to reassure Cpl. Schalit's parents that he is alive and well and will be writing them a letter soon," said Carter. He also reported that Hamas would accept any deal negotiated by Palestinian Authority President Mahmoud Abbas, even one they disagreed with, as long as it was approved by the Palestinian people through a referendum. "Let me underscore the significance of the statement. It means that Hamas will not undermine Abbas's efforts to negotiate the agreement," said Carter. More to the point, if the Palestinian people, through a referendum, agreed to recognize Israel, then Hamas, in effect, would do so as well, he said. But Hamas spokesman Sami Abu Zuhri in Gaza said Hamas's readiness to put a peace deal to a referendum "does not mean that Hamas is going to accept the result of the referendum." Such a referendum, he said, would have to be voted on by Palestinians living all over the world. They number about 9.3 million, including some 4 million living in the West Bank, Gaza and east Jerusalem. A spokesman for Carter said the former president had already left the country and had no response to the comment. But during his speech, Carter acknowledged that he had failed in some respects during his talks with Hamas. The group had rejected his suggestion for a 30-day unilateral cease-fire, he said. "They met all day yesterday to consider this proposal. They finally decided that they were dependent on Egypt as an intermediary, and that progress which had been made already with Egypt should prevail. They couldn't terminate unilaterally, because they didn't trust Israel to follow up by lessening their attacks on Gaza and the West Bank," said Carter. Separately, Carter said that Hamas wants to negotiate an agreement with Abbas to create a government of national consensus with a unified professional security force for the West Bank and Gaza. The cabinet would be composed of technocrats, until another election was held. Hamas has also proposed that the Rafah crossing between Egypt and Gaza be reopened with the help of EU monitors, as it was in the past, except that this time, Egypt, not Israel, would control it. With respect to Syria, where Carter met with President Bashar al-Assad and senior officials, Carter said that Syria wants to conclude a peace agreement with Israel as soon as possible. "I was impressed with their eagerness to complete an agreement on the Golan Heights. He [Assad] said that the only major difference in starting good faith talks was that Israel insisted that there be no public acknowledgement that the talks are going on, whereas Syria insisted that the talks being conducted would not be a secret." Carter said that 85 percent of the differences had been resolved, including borders, water rights, security zones and the presence of international forces. He chastised the US for opposing talks between Syria and Israel. Syria wants the US to play strong role, and "I hope that it will be done," said Carter. He said that he asked the Syrians about the fate of Israeli soldier Guy Hever, who went missing in 1997, while in the area of the Golan Heights. There are those who believe he is being held by Syria. Carter said the Syrians had no evidence of his whereabouts. They also said they knew nothing about the fate of kidnapped soldiers Ehud Goldwasser and Eldad Regev, both of whom were abducted by Hizbullah in July 2006. AP contributed to this report.