"As a gesture of goodwill towards the Palestinians, I will bring before the Israeli cabinet a proposal to free 250 Fatah prisoners who do not have blood on their hands, after they sign a commitment not to return to violence," Olmert said.
"It is important for every Palestinian to understand that we are extending a hand to those who are willing to have peace and reconciliation with us," he said.
"There is no other solution than two states living in peace and security."
Olmert added that Israel would keep pledges made after Abbas sacked Hamas from the government, to end economic sanctions and hand over hundreds of millions of dollars in Palestinian tax revenues as well as to ease travel restrictions in the occupied West Bank.
"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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He also said he was willing to resume a US-sponsored programme of fortnightly talks on efforts to found a Palestinian state, despite Hamas's control of Gaza.
"I'm optimistic that, especially in these turbulent days ... an opportunity has been created to seriously move forward with the regional peace process. I don't plan to let this opportunity slip away," Olmert said.
Hosni Mubarak, the Egyptian president, and King Abdullah of Jordan went into the summit aiming for more, wanting Israel to withdraw from the Palestinian cities in the West Bank and committing to the full implementation of the previously signed accords.
Abbas's short-term demands included an end to all work on Jewish settlements in Palestinian territory and on the wall or fence that Israel is building through the West Bank.
Israel should also release prisoners, remove checkpoints and transfer frozen tax revenues to the Palestinians, he said.
Said Abbas: "I look to ... Prime Minister Olmert to start serious political negotiations, according to an agreed timeframe, with the aim of setting up an independent Palestinian state. My hand is stretched out to the Israeli people."
Hamas, excluded from the meeting, said the leaders were chasing a mirage.
"[The summit] did not give our people anything new except some talk about some money, which was stolen from us," said Hamas official Sami Abu Zuhri.
Mushir al-Masri, a member of the Hamas majority in the frozen Palestinian parliament, said: "The only beneficiary of these summits is the Zionist enemy.
"It is surprising that at a time when Abbas has shut the door on talks with Hamas he is running and begging for a meeting with Olmert."