Talks resumed in July after a three-year hiatus but made little progress.
The latest round was halted by Israel last week after the main Palestinian factions announced a political pact.
US Secretary of State John Kerry meanwhile has issued a statement denying he believed Israel could become "an apartheid state" after drawing criticism over recorded remarks.
On Monday, in comments captured in a recording of a closed-door meeting, he warned that Israel risked becoming "an apartheid state" if a two-state solution was not reached soon."A two-state solution will be clearly underscored as the only real alternative," Mr Kerry said, according to the comments published in the Daily Beast, which published his comments.
"Because a unitary state winds up either being an apartheid state with second-class citizens - or it ends up being a state that destroys the capacity of Israel to be a Jewish state."
But in his statement released early on Tuesday, he said: "I do not believe, nor have I ever stated, publicly or privately, that Israel is an apartheid state or that it intends to become one."
"If I could rewind the tape, I would have chosen a different word to describe my firm belief that the only way in the long term to have a Jewish state and two nations and two peoples living side by side in peace and security is through a two-state solution," he added.
DisagreementsThe failure of the talks puts into doubt the achievement of a two-state solution says the BBC's Middle East editor Jeremy Bowen.
Talks between the two sides were already troubled after repeated disagreements over settlement building and the release of prisoners.
Members from Fatah and Hamas celebrated signing a unity deal in Gaza city last week Negotiations were suspended by Israel after the two main Palestinian factions, secular Fatah and Islamist Hamas, signed a reconciliation deal last Wednesday.
The agreement calls for a unity government within weeks.
Israel said it would refuse to negotiate with any party that includes Hamas as a partner. Hamas refuses to recognise Israel and is regarded as a terrorist organisation by Israel, the US and other countries.
Israeli Prime Minister Benjamin Netanyahu told the BBC that Mr Abbas could "have peace with Israel or a pact with Hamas - he can't have both".
At the time the US expressed "disappointment" over the unity deal, but pushed for the talks to continue.
The US is now likely to monitor developments while continuing to push for a resumption of talks says the BBC's UN correspondent Barbara Plett-Usher.
The Palestinians, meanwhile, are likely to pursue statehood through international organisations such as the UN instead of through bilateral talks, our correspondent adds.
