The two leaders were originally scheduled to meet on Tuesday, but the talks were postponed due to technical reasons.
Low expectations
Palestinians in the West Bank appeared largely indifferent to the high-level talks.
Olmert and Abbas had met three weeks ago, but the situation in the West Bank has not improved since then.
At least 15 Palestinians have been killed in the West Bank and Gaza Strip in Israeli military operations in the past three weeks. Israeli checkpoints remain despite a pledge by Israel to remove some of them.
Analyst George Giacaman said: "There is considerable scepticism on part of the Palestinians after the failure of past meetings.
"Also the continued Israeli incursions, assassinations and confiscation of land.
"There is no basic trust in the Israelis' intentions given that also Israel is the one of the few states that its borders have not yet been defined and the Zionist programme in Palestine has not yet finished."