Condoleezza Rice appeared to make good on her promise to deepen American involvement in the Middle East peace process this morning by brokering a three-way summit between the US, Israel and the Palestinians.

Israeli Army Radio reported that Ehud Olmert, the Israeli Prime Minister, agreed to hold talks with the Palestinian President, Mahmoud Abbas, after meeting the US Secretary of State for breakfast in Jerusalem.

A US diplomat travelling with Ms Rice later confirmed the agreement as the American delegation flew from Israel to Egypt today on the next stage of Ms Rice's Middle East tour.

"They have agreed the three of them that they will meet together — Olmert, Abbas and the Secretary of State — in a trilateral meeting to have a conversation about the political horizon," the official said.

"I would expect the meeting to take place let’s say three to four weeks from now... We didn’t agree on a date but the anticipation is that we try to keep this pace of activity," he said.

The plan was announced after Ms Rice met Mr Abbas yesterday and said: "I have heard loud and clear the call for deeper American engagement in these processes. You will have my commitment to do precisely that."

Mr Rice told journalists in Ramallah that it was now time "to look at the political horizon and begin to show to the Palestinian people how we might move toward a Palestinian state".

Ms Rice, in the region to win what support she can for the Bush Administration's decision to send more troops to Iraq, is keen to show that Washington that help revive the peace process, which has been stalled since Ariel Sharon, the former Israeli Prime Minister, adopted the strategy of unilateral withdrawals from the Palestinian territories.

The White House is also intent on propping up the rule of Mr Abbas, whose Fatah faction is in the midst of intense internecine fighting with Hamas, the elected government and Islamist movement. Yesterday Ms Rice promised $85 million (£44 million) in funding for the Palestinian state security services, which report to Mr Abbas, but have long taken sides in factional disputes.

US State Department officials said the funding would not be used to buy weapons, but Mr Abbas said the money was needed to bring an end to the constant friction between Fatah and Hamas, which has claimed 35 lives in the last three weeks and has led neighbouring countries to speak of a possible Palestinian civil war.

Last night it was the turn of King Abdullah of Jordan to warn Washington of the dangerous consequences of Palestinian instability. He met Ms Rice in Amman and urged her to make progress in peace talks because of the threat of three civil wars in the Middle East: in Iraq, Lebanon and among the Palestinians.

If the summit goes ahead, it will be the second substantive meeting of Mr Abbas and Mr Olmert since the Israeli Prime Minister succeeded Ariel Sharon last year. After initially following his predecessor's policy of not talking to the Palestinian government, Mr Olmert then launched a heavy military campaign in Gaza last summer after the kidnap of an Israeli soldier.

The fighting helped trigger the month-long war with Hezbollah in Lebanon, whose uncertain resolution and Israeli casualties left Mr Olmert's Government weakened.

Mr Olmert turned to diplomacy in December, holding surprise talks with Mr Abbas just before Christmas with the aim of securing the release of Gilad Shalit, the kidnapped Israeli solder. At those talks Mr Olmert announced that $100 million (£51 million) in taxes confiscated by Israel would be handed over to the Palestinian authority and that an exchange of Palestinian prisoners for Corporal Shalit was a possibility.

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