JERUSALEM - Jimmy Carter rebuffed a call Wednesday from an Israeli lawmaker to halt his contacts with Hamas, and senior leaders of the Islamic militant group rushed to Egypt in anticipation of a meeting with the former U.S. president.

Carter, who was scheduled to fly to Egypt after wrapping up the first leg of a weeklong Mideast peace mission, has drawn criticism from the U.S. and Israel for meeting officials from Hamas. The group, which opposes peace negotiations and is committed to Israel's destruction, is considered a terrorist organization by Israel and the U.S.

All of Israel's senior political leaders declined to meet Carter, and only the country's ceremonial president, Shimon Peres, made time to meet with him.

Hamas, which rules the Gaza Strip, announced Wednesday that two of its Gaza leaders, Mahmoud Zahar and Said Siyam, were on their way to meet Carter in Cairo.

"Jimmy Carter wants to hear out our point of view," said Salah Bardawil, a Hamas legislator in Gaza. Bardawil was not part of the delegation going to Egypt.

A Carter spokesman refused to comment on the claim, but meeting the officials would be in keeping with Carter's schedule so far: On Tuesday he met a Hamas leader in the West Bank, and on Friday he is scheduled to meet the group's top official, Khaled Mashaal, in Syria.

"I don't think it is possible to have an ultimate peace agreement without the involvement of Syria. And I don't think it will be possible without the involvement of Hamas," Carter told a group of Israeli and Palestinian peace activists, repeating what has become the theme of his visit. "To have them excluded from conversations or consultations I think is counterproductive," he said.

The group included Israelis who lost friends or family in Palestinian attacks, as well as Palestinians who lost loved ones to fighting with Israeli soldiers.

Earlier Wednesday, hardline Israeli politician Avigdor Lieberman tried to persuade Carter from meeting Hamas' top leader in Syria. "Meeting a terrorist like Khaled Mashaal only encourages and increases terrorism," Lieberman told Carter, according to a Lieberman spokesman.

Carter, a Nobel Peace Prize laureate who brokered Israel's historic peace agreement with Egypt three decades ago, is on what he calls a private peace mission to the Middle East.

In addition to Israel and the Palestinian Authority, he is set to visit Saudi Arabia, Egypt, Jordan and Syria. He is scheduled to return to Israel late Sunday, and said he would present a report summing up his tour.

"I'm not a mediator...I'm just exploring possibilities for peace," he said Wednesday.

Carter said Israelis and Palestinians should adopt an unofficial framework for a peace agreement known as the "Geneva Accord," drafted by dovish Israelis and Palestinians in 2003 without government authorization. That agreement endorsed the formation of a Palestinian state on almost all territory captured by Israel in the 1967 Mideast war.

The sides should "adopt the Geneva Accords as Bible, Holy Scripture, so that all can speak with a common voice," Carter said.