But Israeli officials have more immediate hopes that Abbas would use a beefed-up Fatah to rein in Hamas after it seized the Gaza Strip last month, or at least to safeguard the truncated mandate of the government he set up in the occupied West Bank.
"Abu Mazen [Abbas], who now has nothing to lose and in the past had to pander to Hamas and didn't want to fight them, is facing his ultimate test," Meir Sheetrit, the Israeli Interior Minister, said before the summit began at 1pm.
"We hope that these actions will enable and empower him to fulfil his side of the deal," Sheetrit told Israel's Army Radio.
Olmert and Abbas were meeting on Monday at the former's Jerusalem residence. Such summits have been taking place every few weeks, billed by both sides as confidence-building talks.
Later in the day, George Bush, the US president is due to deliver a speech in Washington that a senior aide said would reassert his support for Fatah leading the way to a Palestinian state coexisting with Israel.
The aide said Bush will also speak about the role of Tony Blair as new envoy for the Quartet of Middle East mediators - the US, the EU, the UN and Russia - which convenes on Thursday.
"The refusal by the US, EU et al to deal with Hamas reflects their disrespect for the wishes of the Palestinian people"
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On Sunday Israel handed the Palestinians a list of 189 fighters, most of whom are from Abbas's Fatah party, saying it would stop hunting them if they pledged to stop activities against it.
"All of the 189 people included on the list handed in by Israel" have signed, a Palestinian security official said.
Zakaria Zubeidi, leader of the Al-Aqsa Martyrs Brigades in the northern West Bank town of Jenin, is included in the list.
Zubeidi told the AFP news agency that all Al-Aqsa fighters on the list "have signed a pledge to stop their attacks against Israel."
"The Al-Aqsa Brigades will not be an obstacle to any political project to solve the Palestinian question in a just manner."
Israel has said that if the men respect their promise for three months, and not leave West Bank areas, their names will be removed from its wanted list.
The amnesty is the latest gesture by Israel to strengthen Abbas after forces loyal to him were overrun in Gaza by Hamas a month ago.
"There are no other ways of helping Mahmoud Abbas except to allow modifications in the list of wanted Palestinians," said Matan Vilnai, Israel's deputy defence minister.
Olmert also favours allowing Nayef Hawatmeh, head of the Democratic Front for the Liberation of Palestine (DFLP), to go to the West Bank this week to attend a "crucial" summit of the Palestine Liberation Organisation (PLO).
It would be the first visit by Hawatmeh, who is based in Damascus to the Palestinian territories since they were captured by Israel during the 1967 Six Day War.