His comments come hours after the US admitted that it had failed to get Israel to renew its settlement curbs.
Mr Abbas suspended talks in September after a 10-month halt on Israeli building in the occupied West Bank, excluding East Jerusalem, expired.
The US has vowed to find other ways to bring the two sides together.
The peace talks resumed in Washington in September after a break of almost two years, but broke down just weeks later over the settlement issue.
US sweeteners
Speaking on a visit to Athens, the Palestinian Authority president said there was "no doubt" that the peace talks were in crisis, the AFP news agency reported.
Washington announced on Tuesday that it had abandoned efforts to persuade Israel to renew its settlement freeze, but said that this did not mean the end of US efforts.
Israeli Prime Minister Benjamin Netanyahu's office has released a statement saying Israel is still fully committed to direct peace talks with the Palestinians without pre-conditions, and that all issues, including the status of East Jerusalem are on the table.
But it is now clear that after weeks of trying, the Israeli prime minister has failed to get his fractious coalition to support a new settlement freeze in the West Bank, says the BBC's Rupert Wingfield-Hayes in Jerusalem.
The US government tried extremely hard to persuade right-wingers in Mr Netanyahu's cabinet that it was in their interest, even offering to give Israel 20 F-35 stealth fighters for free as an inducement, but it failed, our correspondent says.
Israeli and Palestinian negotiators are now due in Washington for separate talks with American negotiators.
But the Palestinian leadership is adamant that it will not come back to the negotiating table without a new settlement freeze.
Israel has occupied the West Bank, including East Jerusalem, since 1967, settling close to 500,000 Jews in more than 120 settlements. They are considered illegal under international law, although Israel disputes this.
What is to be done between now and 2SS? | September 17, 2017 |
The settlers will rise in power in Israel's new government | March 14, 2013 |
Israeli Apartheid | March 14, 2013 |
Israel forces launch arrest raids across West Bank | March 14, 2013 |
This Court Case Was My Only Hope | March 14, 2013 |
Netanyahu Prepares to Accept New Coalition | March 14, 2013 |
Obama may scrap visit to Ramallah | March 14, 2013 |
Obama’s Middle East trip: Lessons from Bill Clinton | March 14, 2013 |
Settlers steal IDF tent erected to prevent Palestinian encampment | March 14, 2013 |
Intifada far off | March 14, 2013 |