"The negotiations will continue as long as the settlement (construction) remains frozen, but I am not prepared to negotiate an agreement for a single day more," Abbas told AFP.
Abbas is to give a speech at the UN General Assembly in New York this week about "efforts to end the Israeli occupation of Palestinian land since 1967 to create an independent Palestinian state with Jerusalem as its capital," his spokesman Nabil Abu Rudeina said.
Israel and the Palestinians began long-awaited peace negotiations under US mediation on September 2.
But so far Israel has stubbornly refused to extend the partial 10-month ban on new construction, and the Palestinians have vowed to pull out of the talks if building resumes.
Speaking en route to New York on Monday, Abbas stressed he was "not opposed to a settlement freeze for a month or two" and that it was possible "to conclude a peace deal on all final status issues if the settlement freeze is extended."
"If Israel stops the settlement and shows goodwill, then we can reach an agreement on borders and security, and agreement on other matters like the status of Jerusalem, water and settlements will follow" in due course, he told AFP.
The Palestinian leader's comments came a day after Prime Minister Benjamin Netanyahu told ministers the settlement moratorium will end as planned.
"Last week, I held political talks in (the Red Sea resort of) Sharm el-Sheikh and Jerusalem. I can't give any detail about the content of the talks because of its sensitivity. What I can say is that regarding the freeze, there has been no change in our position," Netanyahu said.
September 26 deadline
The two rounds of talks, which brought together Abbas, Netanyahu and US Secretary of State Hillary Clinton, failed to break the impasse.
Palestinian officials said on Sunday that efforts were under way to arrange a meeting between Abbas and US President Barack Obama.
Speaking to AFP on Monday, Abbas reiterated the issue of Palestinian prisoners in Israeli jails should be resolved within the framework of any agreement.
Netanyahu's office said he has no plans to head to the United States this week, but President Shimon Peres and Defense Minister Ehud Barak are already there, with Peres due to address the UN summit, and Barak holding talks with US officials.
The deadline for the end of Israel's freeze on settlement construction is widely accepted as September 26, exactly 10 months and a day after the original cabinet decision.
But the Israeli military order regarding the moratorium states it will only close at midnight on September 30.