Israeli Prime Minister Ehud Olmert and Palestinian leader Mahmoud Abbas have met, amid pressure from the US to find a way to restart peace talks.
Mr Olmert has said Israel is ready to make "painful" concessions
The meeting in Jerusalem was the first in a series of fortnightly talks they agreed on during a visit last month by US Secretary of State Condoleezza Rice.
Palestinian group Hamas dismissed the talks as a photo opportunity.
Their next meeting in two weeks is likely to be in the West Bank town of Jericho, both sides indicated.
"It was a positive meeting, part of the ongoing dialogue which helps build confidence between the Israeli and Palestinian leadership," Mr Olmert's spokeswoman, Miri Eisin, was quoted as saying by Reuters news agency.
Chief Palestinian negotiator Saeb Erekat said: "This meeting is only the beginning. I don't think one meeting can solve all the problems."
Peace talks have been largely stalled for six years, and aides for both Mr Abbas and Mr Olmert lowered any expectations that Sunday's meeting would be able to achieve anything substantial.
However, one senior Israeli official said that when the alternative is to do nothing, even the tiniest amount of progress is welcome.
Before the talks, Mr Olmert said Israel was ready to talk to Arab League nations on a recently revived Middle East peace plan.
"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," Mr Olmert said.
The Saudi plan, created in 2002, was revived during the Arab League summit last month.
SAUDI MIDDLE EAST PLAN
First adopted by Arab League in 2002
Calls for "full Israeli withdrawal from all the Arab territories occupied since June 1967"
Calls for Israel's "acceptance of an independent Palestinian State, with East Jerusalem as its capital"
All Arab states would establish "normal relations... with Israel" and "consider the Arab-Israeli conflict ended"
Calls for a "just solution to the Palestinian refugee problem"
Mr Olmert signalled earlier this month that he would attend a regional conference to discuss the peace plan if one was called.
It offers Israel normalisation of ties with Arab states if it pulls out of all Arab land it occupied in 1967 and agrees a "just solution" for Palestinian refugees.
Although it was rejected by Israel five years ago, Mr Olmert said last month his country was ready to make "big and painful" concessions to advance the peace process.