His office said he rejected a White House proposal to stop pushing for a formal resolution condemning settlements and accept instead a non-binding statement calling on Israel to freeze construction on land the Palestinians claim for a state.
His response was given on Friday during a telephone call between the Palestinian leader and US Secretary of State Hillary Clinton, the office said.
"There is no change in the Palestinian and Arab position about the proposal presented to the UN Security Council condemning Israeli settlement on Palestinian land," it read.
One senior Palestinian official, speaking on condition of anonymity, told AFP the offer, made in an hour-long phone call from US President Barack Obama, was accompanied by veiled threats of "repercussions" if it were refused.
"President Obama threatened on Thursday night to take measures against the Palestinian Authority if it insists on going to the Security Council to condemn Israeli settlement activity, and demand that it be stopped," the official said.
"There will be repercussions for Palestinian-American relations if you continue your attempts to go to the Security Council and ignore our requests in this matter, especially as we suggested other alternatives," the official quoted Obama as telling Abbas.
The US president was referring to a package of incentives laid out earlier this week aimed at persuading the Palestinians to withdraw their support for the draft resolution, which is to be put before the Security Council later on Friday.
Despite his decision, Abbas was meeting on Friday evening in Ramallah with the executive committee of the Palestine Liberation Organisation (PLO) and the central committee of his Fatah movement to discuss the latest developments.
The draft condemns Israeli settlement activity in line with the policy of the international community, including the United States -- but Washington does not believe such issues should be tackled within the Security Council.
The Security Council session opens in New York at 3:00 pm (2000 GMT).
After the Palestinians rejected the initial US offer, Obama rang Abbas late on Thursday to suggest that the Security Council make a call for a settlement freeze.
During the conversation, Abbas rejected that proposal too.
"Stopping settlement activity is a Palestinian demand that will not be taken back because it was the reason the peace process fell apart," the Palestinian official quoted him as saying.
"It was a decision taken by the Palestinian leadership and the Palestinian people are sticking to this demand."
It was not immediately clear at what stage in the phone call Obama warned Abbas against turning him down.
Abbas's rivals, the militant Islamic Hamas movement, said that the exchange proved its long-held contention that the White House was not an honest broker in the dispute with Israel.
"This confirms the total support by the American administration for the arbitrary policy of the occupation government," Hamas spokesman Fawzi Barhoum told AFP in the Gaza Strip.
US-brokered peace negotiations between Israel and the Palestinians stalled in late 2010 after the expiry of a temporary freeze on Jewish settlement building in the West Bank.
Efforts by Washington to coax Israel into reimposing a freeze collapsed in December, and the Palestinians are refusing to continue negotiating while Israel builds on land they want for their promised state.
The United States, which regularly uses its Security Council veto power to stop anti-Israeli initiatives, is very keen to avoid the vote because it does not want to be forced to cast a veto.
Should it do so, it would be the first time the United States has used its veto power since Obama took office in January 2009.
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