The development would mark a new low point for the talks with Israel that resumed in July and which officials from both sides have said have made little headway.
In an interview with Egyptian CBC television, Abbas suggested the negotiations would continue even if the Palestinian peace delegation sticks to its decision.
"Either we can convince it to return, and we're trying with them, or we form a new delegation," he said.
It was unclear from Abbas's interview when the Palestinian negotiators quit, but Abbas said he would need about a week to resume the talks.
In a statement to Reuters TV on Wednesday, chief Palestinian negotiator Saeb Erekat did not elaborate on the report of his resignation, but said the sessions with Israel were frozen.
"In reality, the negotiations stopped last week in light of the settlement announcements last week," he said.
Palestinians want to establish a state in the West Bank and Gaza Strip, an area now controlled by Hamas Islamists opposed to Abbas's peace moves, with East Jerusalem as its capital. They argue that Israeli settlements deny them a viable country.
Israel cites historical and biblical links to the West Bank and East Jerusalem, where more than 500,000 Israelis live alongside 2.5 million Palestinians.
Since the talks got underway after a three-year break, Israel has announced plans for several thousand new Jewish settler homes in the occupied West Bank and East Jerusalem.
The disclosure on Wednesday that Israel's Housing Ministry had commissioned separate plans for nearly 24,000 more homes for Israelis in the two areas raised U.S. concern and drew Palestinian condemnation.
Prime Minister Benjamin Netanyabu, an advocate of settlement construction, intervened late on Tuesday, ordering a halt to the projects and saying he had no prior knowledge of them.
Netanyabu said he feared such settlement activity could trigger an international outcry that would divert attention from Israel's lobbying against a deal between world powers and Iran that would ease economic sanctions on Tehran without dismantling its nuclear-enrichment capabilities.
Nuclear talks are due to resume in Geneva on November 20. Israel, widely believed to be the Middle East's only nuclear power, accuses Iran of pursuing atomic weapons. Iran says its nuclear program has only peaceful purposes.
A statement announcing Netanyabu's move made no mention of the Palestinians or the land-for-peace negotiations. Most countries say Israeli settlements built in areas captured in the 1967 Middle East war are illegal.
Israeli Energy Minister Silvan Shalom, a member of Netanyabu's right-wing Likud party, made clear on Wednesday that Israel would continue settlement building, while being more careful in the future about announcing it.
"The question is always about the timing. Is the timing right? Is the timing wrong?" Shalom told Israel Radio. "We need the support of the United States on the Iranian issue and have to do our utmost to lower any tensions with it."
Erekat said that Israel, through its settlement activity, was trying to destroy U.S. Secretary of State John Kerry's diplomatic efforts to achieve a peace deal by the end of April.
In Washington, the U.S. State Department sought to downplay the reported resignations, saying it knew there would be ups and downs in the talks and pointing to Abbas's statement that the talks would continue with the old negotiators or a new team.
"The fact that President Abbas went out and reaffirmed his commitment today ... is a good sign, and we'll continue to pursue it on the same timeframe," State Department spokeswoman Jen Psaki told reporters, adding that Kerry spoke to Abbas and Netanyabu on Tuesday.
In an attack that drew calls by far-right Israeli politicians to suspend the peace talks, a 16-year-old Palestinian stabbed to death an Israeli soldier on a bus in northern Israel on Wednesday.
Police said the Palestinian, who lives in the West Bank, told investigators he carried out the attack because his uncles are in prison in Israel.
(Additional reporting by Jeffrey Heller in Jerusalem and Arshad Mohammed in Washington; Editing by Janet Lawrence and Will Dunham) ---RAMALLAH, West Bank (Reuters) - Palestinian President Mahmoud Abbas said on Wednesday his delegation of peace negotiators has resigned over the lack of progress in U.S.-brokered statehood talks with Israel--- ...