Palestinian negotiator Saeb Erekat said Blair's mission will complement direct talks between Israel and the Palestinians. ''What will make the requirement for peace at the end of the day will be the bilateral Israeli-Palestinian tracks,'' he said after Blair's talks.
He said the envoy would return to the Mideast in September.
Another Palestinian official said Blair informed Abbas that his official mandate was to provide an economic horizon for Palestinians but that he would try to use his good relations with Israel and Bush to give new life to the peace process. The official, who attended the meeting but was not authorized to brief the press, spoke on condition of anonymity.
Blair's trip is part of a flurry of diplomatic efforts to restart peace talks after a seven-year lull.
On Wednesday, the Jordanian and Egyptian foreign ministers will arrive in Israel to formally present an Arab peace initiative that envisions full Arab recognition of Israel in return for lands the Jewish state captured in the 1967 Middle East war.
Blair takes up his task at a promising time. The Palestinian uprising has largely fizzled and Abbas has installed a pro-Western government in the West Bank.
Blair's mandate from the Quartet was limited to helping the Palestinians develop their economy, build governing institutions and laying the groundwork for statehood. He was instructed to leave aside ''final-status'' issues on resolving the conflict, such as borders, Palestinian refugees and the governance of Jerusalem — a move that raises questions about how effective he can be.
His task also has been complicated by Palestinian infighting that led to the forcible takeover of Gaza by the Islamist Hamas movement in a bloody five-day war last month. Abbas' Fatah movement now spearheads a moderate government in the West Bank while Hamas has control of Gaza.
The Quartet has shunned Hamas, which the U.S. and EU consider a terrorist group.
Hamas, which won Palestinian legislative elections last year, warned that it cannot be ignored. ''It will lead to nothing but failure,'' said Hamas spokesman Fawzi Barhoum.