The two men have been holding regular meetings since November 2007
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Israeli PM Ehud Olmert has met Palestinian leader Mahmoud Abbas for peace talks, a day before Mr Olmert's party is due to replace him as leader.
The US government wants to see a full peace deal reached before President George W Bush leaves office in January.
A spokesman for Mr Olmert described the discussions as "serious" and said the two leaders would meet again soon.
Mr Olmert, who denies corruption claims, says he will step down after his Kadima party chooses his successor.
The party votes on Wednesday and the front-runners to succeed him are Foreign Minister Tzipi Livni and Transport Minister Shaul Mofaz.
But Mr Olmert may stay on as caretaker prime minister until a new coalition government is formed, which could take weeks or even months.
'Work needed'
Mr Olmert and Mr Abbas have been meeting regularly since new dialogue was launched at a peace conference in the US in November 2007.
Core issues up for discussion are the status of Jerusalem, the borders of a Palestinian state, settlements in the West Bank, refugees, security and water resources.
But there has been little visible progress and it is widely accepted by Israelis and Palestinians that an agreement by January is increasingly unlikely.
Mark Regev, spokesman for the Israeli prime minister, did not disclose details of the discussions.
But he said they would continue as long as Mr Olmert "remains prime minister of Israel, and he does so until a new government is sworn in".
"We have come a long way but more work needs to be done," he added.
The two men will meet again once Mr Abbas returns from the opening ceremony of the annual UN General Assembly, where he is scheduled to meet Mr Bush.
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