"The land of Israel belongs to both Jews and Palestinians - as long as there are people who reject this fact, the conflict will never be solved"
Iskander, Boston, US
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The UN, US, EU and Russia want the Palestinian government to recognise Israel, renounce violence and accept existing interim peace deals.
An Israeli government official said Olmert "presented the Quartet conditions and said that Israel cannot co-operate with a government or with a part of a government that does not respect these conditions".
However, Olmert has promised to keep a channel of communication open with the Abbas, a policy promoted by the US, which plans to send Condoleezza Rice, its top diplomat, back to the region in the next few weeks.
Olmert and Abbas spent part of the session in face-to-face talks without aides present and agreed to talk "on a regular basis", an Israeli official said.
Before the meeting, the third Olmert and Abbas have held since December, both sides played down expectations of a breakthrough. Neither leader made statements at the start or end of the talks.
Last month's Saudi-brokered Palestinian coalition agreement that calmed weeks of warfare between Hamas and Abbas's Fatah faction contains a promise to "respect" previous Israeli-Palestinian accords.
It does not, however, commit the incoming government to abide by those pacts, nor to accept international conditions which are key to the resumption of aid to the Palestinian Authority, which was cut off by the West after Hamas came to power more than a year ago.
Ismail Haniya, the Palestinian prime minister from Hamas, said a unity government could be announced as early as Monday.
In remarks before the session, Olmert made comments before the meeting that appeared to open the door to exploring whether a 2002 Saudi peace initiative could serve as an alternative track towards an Israeli-Palestinian settlement.