(Adds end of meeting, Israeli, Palestinian comments) By Jeffrey Heller JERUSALEM, April 15 (Reuters) - Israeli Prime Minister Ehud Olmert and Palestinian President Mahmoud Abbas launched a U.S.-initiated series of meetings on Sunday, bypassing some of the most contentious issues of the Middle East conflict. But in an apparent nod towards an alternative track involving the Arab League and a 2002 Saudi-initiated peace plan, Olmert told his cabinet he was "willing to hold a dialogue with any grouping of Arab states about their ideas". Neither Olmert nor Abbas appears to be in a position to make bold moves towards a final peace deal. Olmert's approval rating is in single digits and Abbas's Fatah faction shares power with Hamas, an Islamist group that does not recognise Israel. The two-hour meeting, over lunch at Olmert's Jerusalem residence, was the first between the two men since they agreed during a visit by U.S. Secretary of State Condoleezza Rice last month to convene every two weeks. "It was a positive meeting, part of the ongoing dialogue which helps build confidence between the Israeli and Palestinian leadership," Olmert spokeswoman Miri Eisin said. "The next meeting will be in a couple weeks and there's a strong possibility it will be in (the West Bank town of) Jericho." Saeb Erekat, a senior Abbas aide, said: "This meeting is only the beginning. I don't think that one meeting can solve all the problems ... or (reach) the political horizon." Six years after Israel and the Palestinians last held final-status talks, Washington is seeking to shape what it terms a "political horizon" for both sides while it tries to enlist Arab support for its own policies in Iraq and towards Iran. "They talked a bit about the political horizon," Eisin said, citing "economic ideas that can be implemented". CORE ISSUES Olmert aides said before the session he was prepared to discuss the legal, economic and governmental structures of a future Palestinian state in the meeting with the moderate Abbas, who formed a unity administration with Hamas last month. "We will not discuss the core issues of the conflict -- the issue of (Palestinian) refugees, Jerusalem and borders," Olmert said in broadcast remarks at the weekly cabinet meeting. Eisin said "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. She said Olmert did not disclose what he and Abbas discussed in an hour-long private talk. On the eve of the meeting, Hamas spokesman Fawzi Barhoum dismissed the meeting as "useless" and a "photo opportunity". While pursing a dialogue with Olmert, Abbas is also pushing him to hold talks based on the 2002 Arab peace initiative. 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 plan. Olmert said earlier on Sunday he saw "positive elements" in the proposal offering Israel relations with all Arab states if it withdrew from all land occupied in the 1967 Middle East war, allowed a Palestinian state and reached an acceptable solution for Palestinian refugees. Aides said on Saturday that Olmert, whose political future could hinge on the interim report later this month of an Israeli inquiry into last year's inconclusive Lebanon war, was "leaning in favour" of contacts with an Arab League working group. Eisin said Olmert also pressed Abbas to do his utmost to help secure the release of an Israeli soldier seized by Gaza militants last year. She said the Israeli leader promised Abbas to do more to ease travel restrictions against Palestinians in the West Bank and Gaza. (Additional reporting by Wafa Amr in Ramallah, Nidal al-Mughrabi in Gaza, Jonathan Saul and Adam Entous in Jerusalem)
