Hamas said today it would accept a Palestinian state on land occupied in the 1967 war, but it would not explicitly recognise Israel.

Khaled Meshaal, the leader of Hamas, said the group would "respect Palestinian national will even if it was against our convictions", an apparent reference to a referendum on a peace deal.

His comments came at a news conference in Damascus, Syria, after a rare series of meetings between the former US president Jimmy Carter and Hamas Islamists in the West Bank, Cairo and Damascus.

At an earlier press conference, Carter said Hamas would accept a two-state peace agreement with Israel as long as it was approved by a Palestinian referendum or a newly elected government.

Carter, who spoke in Jerusalem, said Hamas had told him it would support the results of a referendum or election on a final-status peace agreement negotiated by the Palestinian president, Mahmoud Abbas, even if Hamas itself opposed the agreement.

The former president and Nobel peace prize-winner admitted he had failed to convince Hamas to begin a unilateral ceasefire in Gaza, the scene of continued violence.

"If President Abbas succeeds in negotiating a final-status agreement with Israel, Hamas will accept the decision made by the Palestinian people and their will through a referendum ... or by a newly elected Palestinian national council ... even if Hamas is opposed to the agreement," Carter said in a speech at the King David hotel. "Verbatim, this is their language," he said.

Carter insisted he was not acting as a mediator and he noted his visit was not endorsed by either the Israeli or the US government, so there was little sign it would advance the so-far fruitless Middle East peace talks between Abbas and the Israeli prime minister, Ehud Olmert.

He acknowledged that Hamas still refused to recognise explicitly Israel's right to exist, or to renounce violence, or to recognise previous peace agreements. The movement did not agree to speed the release of an Israeli corporal captured two years ago, although it did tell Carter it would let the soldier, Gilad Shalit, write a new letter home to his parents to prove he was still alive.

Carter condemned attacks by Hamas as "despicable" and "acts of terrorism". Yet he sounded encouraged by his talks, which included meetings with Meshaal and the most powerful Hamas leader in Gaza, Mahmoud Zahar.

"They said they would accept a Palestinian state on the 1967 borders if approved by Palestinians and they would accept the right of Israel to live as a neighbour next door in peace provided the agreements negotiated by Prime Minister Olmert and President Abbas were submitted to the Palestinians for their overall approval, even though Hamas might disagree with some terms of the agreement," Carter said.

The Hamas position reflected a key agreement known as the Prisoners' Document, which Hamas signed with its rival Fatah, led by Abbas, two years ago. However, that agreement was overtaken by a near civil war between the two rival groups.

The Hamas leaders also told Carter a "national reconciliation" between Hamas and Fatah was necessary for any peace agreement to work, even though the two sides appear a long way from a rapprochement.

One Hamas spokesman in Gaza, Sami Abu Zuhri, immediately cast doubt over Carter's words when he said the idea of a referendum on a peace agreement "does not mean that Hamas is going to accept the result of the referendum". He said Palestinians living abroad would have to take part in the vote, not only those in the occupied territories.

Carter said it was widely acknowledged on the ground that any progress under the current peace talks, which were launched in Annapolis last November, was so far "of no significance".

"Since Annapolis the peace process has regressed," he said, citing the continued growth of Jewish settlements in the West Bank and the economic blockade on Gaza.

He argued there should be talks with Hamas in order to resolve the Middle East conflict. "We believe the problem is not that I met with Hamas in Syria," he said. "The problem is that Israel and the United States refuse to meet with these people who must be involved."