Ehud Olmert said that Israel would release prisoners, withdraw from West Bank Jewish settlements and ease checkpoints if Palestinians abandoned violence.

But although he held out the prospect of “real, open, genuine and serious dialogue” with Mahmoud Abbas, the Palestinian President, Mr Olmert’s offer had three conditions. They were for Palestinians to replace Hamas with a new government committed to recognising Israel, implement President Bush’s long-delayed “road map” and release the captured Israeli soldier Gilad Schalit.

“When Gilad Schalit is released and returned to his family, safe and sound, the Government of Israel will be willing to release numerous Palestinian prisoners — including ones who were sentenced to lengthy prison terms,” Mr Olmert said.

The Prime Minister infuriated right-wing critics by offering to reduce roadblocks, evacuate “many territories” in the West Bank and look forward to an “independent and viable Palestinian state . . . with full sovereignty and defined borders”. The key to a resumption of Israeli-Palestinian dialogue is talks in Cairo between Hamas’s supreme leader, Khaled Mashaal , and Egyptian mediators. They are trying to broker a deal that would secure the release of Corporal Schalit in exchange for hundreds of Palestinian prisoners, and lead to the formation of a Palestinian national unity government.

In Israel, rightwingers criticised Mr Olmert’s overtures. Yuval Steinitz, a Likud MP, said: “The Prime Minister is offering hills and mountains . . . to a Hamas Government and parliament which breached all agreements and ceasefires.”

However, Mohammed Eid Shubair, the academic widely tipped to take over from the Hamas leader Ismail Haniya as prime minister, confirmed that a government led by him would allow President Abbas to negotiate with Israel.

Sidestepping the crucial issue of whether such a national unity administration would recognise the Jewish state — a precondition to ending the international embargo — Dr Shubair told The Times: “I think the file of politics is in the hands of Mr Abbas. As I understand it from him, all these issues are going to be dealt with by the Palestine Liberation Organisation and the Government should take care of internal affairs.”

Palestinians in Gaza were sceptical about Mr Olmert’s remarks, believing them timed to satisfy President Bush before his arrival in the Middle East tomorrow to meet Nouri alMaliki, Iraq’s Prime Minister.

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