Abbas appealed to Olmert not to pass up "this historic opportunity" to make peace with the Palestinians.
"I invite you to start serious political negotiations according to an agreed calendar, with the aim of establishing an independent Palestinian state with Jerusalem as its capital, existing alongside Israel," Abbas told the summit.
In return, Olmert stressed he was "extending a hand" of reconciliation to moderate Palestinians.
"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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"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 told Abbas, Hosni Mubarak, the Egyptian president, and King Abdullah of Jordan.
"There is no other solution than two states living in peace and security," Olmert said.
However his offer came with conditions as he said he would ask his cabinet to approve the release of 250 members of Abbas's secular Fatah movement "without blood on their hands" but stressed that those prisoners must commit to renounce "terrorism."
'Mending the rift'
Hosni Mubarak, the Egyptian president, made a call for inter-Palestinian dialogue to mend the rift.
"Our deliberations today affirmed the parallel need to end disagreements, and unify the Palestinian ranks through dialogue," the Egyptian leader said.
He said "the resumption of dialogue between all the children of Palestine, and the achievement of a common position that speaks for its people and its cause, is an immediate requirement that can bear no delay."
Ismail Haniya, the sacked prime minister, said on Monday that Hamas movement was ready to immediately take part in inter-Palestinian talks.
"Prime minister Ismail Haniya favourably received the appeal launched by President (Hosni) Mubarak at Sharm el-Sheikh in favour of a revival of inter-Palestinian dialogue," Haniya's office said in a statement.
"Hamas for its part is disposed to immediately take up this dialogue" with Fatah movement, it said.
Speaking before the summit, Ahmed Aboul Gheit, Egypt's foreign minister, was hopeful that progress on the Palestinian issue would be made.
"The aim of the meeting is to regain confidence between the Israeli and the Palestinian sides, achieve the return to confidence building between them through agreed upon measures that should be strictly applied until the road is open to restart negotiations between the two sides," he said.
But Olmert cautioned that there would be no "dramatic breakthrough", rejecting Palestinian calls to start talks on a peace treaty.
An aide to Olmert said that negotiations on a final Israeli-Palestinian peace deal were not going to be discussed, despite being urged by Abbas' Fatah and other Arab countries to take immediate advantage of the Hamas expulsion from the coalition government.
David Baker, Olmert's aide, said Israel was "not ready yet to go into final status negotiations."