Former US President Jimmy Carter has said that Hamas is prepared to accept the right of Israel to "live as a neighbour next door in peace".
After meeting Hamas leaders last week in Syria, he criticised the US and Israel for refusing to meet the group.
US Secretary of State Condoleezza Rice has challenged Hamas to prove its goodwill by renouncing violence.
After Mr Carter's remarks, Hamas leader Khaled Meshaal stressed that Hamas would not formally recognise Israel.
But he told a news conference in the Syrian capital, Damascus, that Hamas would accept a Palestinian state on the land occupied by Israel in the 1967 war.
Meanwhile, the Israeli army has launched a formal investigation into the death of a Reuters cameraman killed in the Gaza Strip last week.
Two Palestinians died in Israeli air strikes in the territory on Monday: one person in the southern city of Rafah and a Hamas militant at Beit Hanoun, a border town from where rockets are often fired at Israel.
Israeli Prime Minister Ehud Olmert refused to see Mr Carter, as he ended his regional visit in Jerusalem.
In a speech in the city, Mr Carter said Israeli-Palestinian peacemaking had "regressed" since the US hosted Middle East talks in November at Annapolis.
Hamas indicated... that if Israel is willing to have a mutual ceasefire... they will accept it
He defended his talks in Damascus with exiled Hamas political leader Mr Meshaal.
"The problem is that Israel and the United States refuse to meet with someone who must be involved," he told Israel's Council on Foreign Relations.
Hamas had reiterated its position that it could accept an Israeli state within its pre-1967 borders and live in peace with Israel, he said.
"Hamas indicated... that if Israel is willing to have a mutual ceasefire and a renunciation of violence in Gaza and in the West Bank, they will accept it, and as a first step they would even accept just limiting that to Gaza," he said, speaking to the BBC's Newsnight programme.
Israel, the US and the European Union regard Hamas, which controls the Gaza Strip, as a terrorist organisation.
Hamas is officially dedicated to the destruction of Israel and the creation of an Islamic state in Israel, the West Bank and Gaza.
Call for proof
Mr Carter also said the release of Israeli soldier Gilad Shalit, captured by Hamas and other militant groups during a raid into Israel two years ago, was being held up by the lack of direct communication between Israel and Hamas.
Mr Carter said the difficulty was in agreeing the identity of the Palestinian prisoners to be released in return.
He said Egyptian officials had told him that Israel had agreed to release 1,000 prisoners but accepted only 71 names on a list of hundreds of prisoners submitted by Hamas.
Khaled Meshaal told reporters on Monday that Hamas had agreed to pass a message from Corp Shalit to his family.
Speaking in Manama on a tour of the Middle East, Ms Rice said Hamas should show their willingness to make peace by releasing Corp Shalit and halting rocket attacks on Israel.
She also called on the group to recognise the legitimacy of the Palestinian Authority, whom they ousted from Gaza last summer.
Israel has said it will investigate the death of Palestinian Reuters cameraman Fadel Shana, who died with several other civilians in Gaza last Wednesday.
New York-based Human Rights Watch says it has evidence an Israeli tank team fired either recklessly or deliberately at Mr Shana.
The Israeli army denies deliberately targeting civilians.
Israeli Human rights group B'tselem has reported that Mr Shana was killed by a flechette shell, which rains down thousands of small metal darts.
The group called for use of the shell to cease immediately and for a criminal investigation of the event.
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