Israeli Prime Minister Ehud Olmert and Palestinian President Mahmoud Abbas held talks in Jerusalem on Monday.

The two leaders met a few hours after U.S. Secretary of State Condoleezza Rice's departure from the region.

An Israeli official said major progress was achieved on the issue of the permanent borders of a future Palestinian state and the security arrangements during the meeting.

Israeli government spokesman Mark Regev described Monday's talks as possibly the most serious talks with the Palestinian side.

"These talks are serious, quite possibly the most serious talks an Israeli side has ever had with the Palestinian side."

The peace talks between Israel and the Palestinians are to be based on US backed "roadmap", a peace plan that sets out a phased process leading to the formation of a Palestinian state.

As interim measures, Israel is supposed to halt settlement activity and take steps to improve the freedom of movement for Palestinians, while the Palestinians are supposed to dismantle militant groups.

However, there has so far been little visible progress in the talks.