JERUSALEM – Just hours after former President Jimmy Carter trumpeted Hamas' agreement to let Israel "live as a neighbor," the same terrorist leader he met with face-to-face vowed not to recognize the Jewish state.
But Hamas leader Khaled Mashaal did offer Israel a 10-year truce if it withdraws from all lands it seized in the 1967 Arab-Israeli war.
Carter met twice with Mashaal over the weekend.
The former president also said Monday that he would never sit down with Al Qaeda because the terror network has no "redeeming features."
"[Al Qaeda] are not involved in any sort of a fruitful process. They are not recognized by their own people," Carter told FOX News in an interview Monday. "On the other hand, you have to remember Hamas in an honest and open and fair and transparent election were elected the leaders of the Palestinian government."
Carter claimed his meetings with Hamas and Syrian leaders weren't meant to circumvent the Bush administration, nor was it an attempt to formally negotiate with Hamas.
"I'm not undermining anything. I'm not negotiating. ... I'm just here representing myself and the Carter Center. No one else," he said. "My decision was just to talk to people who must be involved in the final peace agreement.
"Syria and Hamas will have to be involved in the long term," he said. "And I thought I could at least talk to them and relay their opinions."
When asked whether he'd ever meet with Al Qaeda, Carter replied, "No, of course not."
"I don't see any redeeming features of Al Qaeda at all," he said.
When making a distinction between Usama bin Laden's terror network and Hamas, which has been in power since the 2006 Palestinian elections, Carter said that Israeli citizens backed his talks with Hamas.
"The Israeli people strongly support what I have done, at least indirectly," he claimed, citing polls that show "that 64 percent of all Israeli citizens strongly support direct talks between the government of Israel and Hamas."
Speaking in Jerusalem, the former president said Hamas is prepared to accept the outcome of Israeli-Palestinian peace talks, provided it is approved in a Palestinian referendum, or by a Palestinian government chosen in new elections.
"We do not believe that peace is likely and certainly that peace is not sustainable unless a way is found to bring Hamas into the discussions in some way," he said. "The present strategy of excluding Hamas and excluding Syria is just not working."
Carter met with top Hamas leaders in Syria for two days last week. His speech capped a nine-day visit to the Mideast designed to break the deadlock between Israel and Hamas militants who rule Gaza.
In the past, Hamas officials have said they would establish a "peace in stages" if Israel were to withdraw to the frontiers it held before the 1967 Mideast War. But it has been evasive about how it sees the final borders of a Palestinian state, and has not abandoned its official call for Israel's destruction.
Israel and the U.S. State Department consider Hamas to be a terrorist group. Israeli officials had shunned Carter during his visit because of his meetings with Mashaal, and other group leaders.
Syria harbors Hamas' exiled leadership in its capital, Damascus, and supports the Lebanese Hezbollah guerrillas who warred with Israel in 2006.
Carter said Hamas wouldn't undermine moderate Palestinian President Mahmoud Abbas' efforts to reach a peace deal with Israel, as long as the Palestinian people approved it in a referendum. In such a scenario, he said, Hamas would not oppose a Palestinian state in the West Bank and Gaza.
Hamas leaders "said that they would accept a Palestinian state on the 1967 borders" and they would "accept the right of Israel to live as a neighbor next door in peace," he said.
The borders he referred to were the frontiers that existed before Israel captured large swaths of Arab lands in 1967 — including the West Bank, east Jerusalem and Gaza.
Israel, which evacuated Gaza in 2005, has accepted the idea of a Palestinian state there and in much of the West Bank, but has resisted Palestinian demands that it return to its 1967 frontiers.
Both the Israeli and U.S. governments disapprove of Carter's overtures to Hamas, which they consider to be a terrorist organization. Over the weekend, Israeli Prime Minister Ehud Olmert said he did not meet with Carter in Israel because he did not wish to be seen as participating in any negotiations with Hamas.
During his trip, Carter met only with Israeli President Shimon Peres and Eli Yishai, one of several deputy prime ministers. Peres scolded Carter for meeting with Hamas, but Yishai, of the ultra-Orthodox Shas Party, said he was willing to meet with Hamas leaders to discuss a prisoner exchange.
Israel says Carter's talks embolden Palestinian extremists and hurt Palestinian moderates as they try to make peace with the Jewish state. Abbas, who rules only the West Bank, is in a bitter rivalry with Hamas.
"The problem is not that I met with Hamas in Syria," Carter said Monday. "The problem is that Israel and the United States refuse to meet with someone who must be involved."
Carter said direct communication between Israel and Hamas could facilitate the release of a captured Israeli soldier, Cpl. Gilad Schalit, who has been held in Gaza for nearly two years.
Israel agrees in principle to trade 1,000 Palestinian prisoners for Schalit, but after back-and-forth talks through Egyptian intermediaries, has approved only 71 of the specific prisoners that Hamas wants freed, he said.
Carter said Hamas has promised to let Schalit send a letter to his parents to assure them he is in good health, and said the militants "made clear to us that they would accept an interim ceasefire in the Gaza Strip."
Carter, however, said Hamas rejected his specific proposal for a monthlong unilateral truce.
"They turned me down, and I think they're wrong," he said.
FOX News' Reena Ninan and The Associated Press contributed to this report.