Mr Abbas said the endeavour was: "aimed at trying to breathe new life into the negotiations".
Mr Abbas said he had not given up on reconciliation but could not "wait forever".
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Had Mr Abbas said yes, it might have been hard for a future Israeli government to back out.
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However, a spokesman for Mr Abbas said the Palestinian leader had told Mr Obama the precondition remained in place.
Speaking on his way to New York, Mr Abbas said he was under "tremendous pressure" to drop his bid.
Mr Abbas said he had no right to like or dislike Israel's democratically elected prime minister as his legitimate interlocutor.
Mr Abbas said he was seeking to agree a ceasefire with all the Palestinian factions, but was prepared to take more forceful action should this fail.
Thanking the US administration for its continuing support for the Palestinian Authority, Mr Abbas said peace with Israel should not be achieved through violence, occupation, settlements, arrests or denial of refugee rights.
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"From our point of view, the boycott of the Palestinians was always an injustice and we have to find a solution to overcome these problems, " Mr Abbas said on Thursday, after meeting German Foreign Minister Frank-Walter Steinmeier.
"Sixty-five years ago on this day, the United Nations General Assembly adopted resolution 181, which partitioned the land of historic Palestine into two states and became the birth certificate for Israel, " Mr Abbas said shortly before the vote in New York.
In a decree carried on Sunday by the official Wafa news agency, Mr Abbas said the move on labelling public documents would help bolster the Palestinian state "on the ground and build its institutions... and its sovereignty over the its land".
But Mr Abbas has said several times that the present intifada against Israel a horribly bloody one compared with the largely unarmed precursor of the 1980s was a mistake.
On Friday, following two days of talks with Israeli Prime Minister Benjamin Netanyahu and Mr Abbas, he said that "hard decisions" would be needed for peace.
But in his joint news briefing with Mr Abbas, he said such problems could not be used "as an excuse to do nothing", and neither side could expect to resolve every outstanding issue before talks resumed.
The real test will be Israel's implementation, said Mr Abbas.
The Israelis said Mr Abbas and his aides seemed unprepared to make that commitment, rehearsing rather their demand that Mr Sharon announce first his unequivocal acceptance of the road map.
And the president said he believes Mr. Abbas would assume that responsibility and that the United States would help him, but he said it was critical that a few people, a few terrorists, a few killers, the president called them, not derail the hopes for peace, hopes that once again seem to have a bit of a momentum after these sessions.
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But Israel's Prime Minister Benjamin Netanyahu called the vote "meaningless", and said that Mr Abbas' address in New York had not been "the words of a man who wants peace".
Documents quoted by the paper are said to show that Mr Abbas bought the vessel from its former owners, a Lebanese shipping company, on 31 August last year.
The Americans are said to be pressing Mr Abbas to present to Mr Sharon serious, practical plans for reining in the terror, at least in the Gaza strip as a first stage.
Mr Abbas's government had taken some action, he said, according to Israeli sources.
Mr Olmert and the Palestinian leader, Mahmoud Abbas, have both said they would have reached a peace deal between them had his term as prime minister not been truncated.
And in an effort to isolate Gaza's rulers, Mr Abbas's PA, which is based in Ramallah, said it would attend international events, such as the recent Arab League summit in Libya, only on condition that Hamas is excluded.
Mr. Abbas has illustrated flexibility on the settlement issue in recent meetings, said U.S. and Palestinian officials, but made clear that he needed concessions from Israel to sell the peace process to his people.
He said peace was necessary, just and possible, and that Mr Abbas and Palestinian Authority Prime Minister Salam Fayyad were "true partners" for peace.
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Mr Abbas, who met Israeli Prime Minister Ehud Olmert in Jerusalem earlier this week, said the new administration was "a first and important step towards bringing the Palestinians together".
After Hamas had said it would release Mr Saadat once it formed a government, Mr Abbas declared in a public lecture on March 7th that he would consider freeing the PFLP leader.
Mr Abbas himself condemned the bombing, offered his condolences to the victims' families and said it did not serve the interests of the Palestinian people something of an understatement considering how a renewed Israeli security clampdown will worsen the penury many Palestinians live in.
Mr Abbas's influential boss, Yasser Arafat, the chairman of the Palestinian Authority, said that nothing tangible was achieved at the summit.
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