The White House denied the existence of a such a letter to the Palestinian Authority president as well as reports of a letter sent by Obama to Israeli President Binyamin Netanyahu, the newspaper said.
The letter to Abbas gave assurances that the U.S. would push for the creation of a Palestinian state within the 1967 borders and land swaps if Abbas agrees to continue direct peace negotiations with Israel, the newspaper said.
The letter to Netanyahu, which reports said he rejected, offered security guarantees to Israel if it agreed to extend a building freeze in West Bank settlements for 60 days, the newspaper said.
U.S. and EU envoys were attempting to salvage the Israeli-Palestinian peace talks, diplomats said.
Catherine Ashton, the EU foreign policy leader, met with Palestinian Prime Minister Salam Fayyad in the West Bank, then went to Jerusalem to meet Netanyahu. U.S. Middle East envoy George Mitchell also was in the region, the BBC reported.
"We are determined to continue our efforts to find common ground between the parties to enable the direct negotiations to continue," Mitchell said.
Ashton and Mitchell were to meet with both Netanyahu and Abbas, Israel Radio said.
The U.S. is incensed over Netanyahu's rejection of the letter drafted by Obama's advisers -- and Netanyahu's advisers -- Haaretz said Friday.
David Makovsky, a senior fellow at the Washington Institute for Near East policy, published details of what he said was Obama's letter to Netanyahu Thursday.
"The draft letter offers a string of assurances to Israel in return for a two-month moratorium extension. More specifically, U.S. officials indicate that the document makes commitments on issues ranging from current peace and security matters to future weapons deliveries in the event that peace-related security arrangements are reached," Makovsky wrote.
Washington agrees not to ask for an extension of the 60-day freeze and says the future of settlements should be dealt with at the negotiating table as part of territorial talks, he wrote.
"Second, the draft letter promises that the United States will veto any U.N. Security Council initiative -- Arab or otherwise -- relating to Arab-Israeli peace during the agreed one-year negotiating period. Third, Washington pledged to accept the legitimacy of existing Israeli security needs and not seek to redefine them. In this context, the draft letter explicitly mentions the need to ensure a complete ban on the smuggling of rockets, mortars, arms, and related items, as well as the infiltration of terrorists into Israel."
A number of Israeli government ministers upset over Netanyahu's rejection of the letter, have demanded he present it to the Cabinet before the Arab League convenes to discuss whether to order Abbas to abandon direct talks, the Israeli dailies said.
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