Offer to discuss Saudi initiative comes after Merkel urges Middle East progress.
The talks were the first since the two men agreed during a visit from the US secretary of state last month to hold meet every two weeks.
Ahead of the meeting both sides played down hopes of a significant breakthrough, saying it was important simply that the two sides were talking.
“Let us respect all religions, civilizations and people that were originated from the Middle East,….and let’s drive for respectable, long lasting and fair solution.”
Miri Eisen, Olmert’s spokewoman, said afterwards: “It was a positive meeting, part of the ongoing dialogue which helps build confidence between the Israeli and Palestinian leadership.”
“They talked a bit about the political horizon,” Eisin said, citing “economic ideas that can be implemented”.
She added that “final-status” issues were not raised in the first half of the session, also attended by Israel’s defence and foreign ministers and Abbas aides.
Olmert did not disclose what he and Abbas discussed in an hour-long private talk.
Saeb Erekat, a senior adviser to Abbas, said: “This meeting is only the beginning. I don’t think that one meeting can solve all the problems … or[reach] the political horizon.”
On the eve of the meeting, Fawzi Barhoum, a Hamas spokesman, had dismissed it as “useless” and a “photo opportunity”.
Ahead of the meeting, Olmert told his weekly cabinet meeting that Israel was ready to talk to Arab nations about their peace plan for the region.
“We are ready to hold talks with any combination of Arab states on their ideas and I would be glad to hear their ideas on the Saudi initiative,” he said.
“I’ll be glad to hear their ideas and for them to listen to ours,” he added. “I hope there will be a chance for such meetings.”
An Arab League summit last month revived a proposal which offers Israel peace and normal ties with Arab countries in exchange for withdrawing from land occupied during the 1967 Six Day War, allowing the creation of a Palestinian state and the return of refugees.
Israel, which initially rejected the plan when it was first unveiled in 2002, has said recently it could provide a basis for talks, provided there are amendments to the refugee issue – something the Arab states have refused.
An Arab League committee of 13 foreign ministers will meet in Cairo on Wednesday to talk about setting up several working groups to promote the 2002 Arab initiative.