Israeli Defence Minister Ehud Barak says there is a "50-50" chance of reaching a deal with Palestinians about Israel's moratorium on building new settlements.
Diplomats are seeking a deal as a 10-month Israeli ban on settlement-building winds down, putting the talks at risk.
The BBC reports settlers in the West Bank are preparing to resume construction on Monday if no deal is reached on an extension.
However, Mr Barak says nobody can let this historic opportunity slip.
Mr Barak said he was heading back to Israel to try to convince members of the Israeli government of the need for a compromise, but that he was not confident of success.
However, he was more upbeat on the prospects for the peace talks, which resumed in September after a 20-month hiatus.
Peace or the continuation of Jewish settlements
Palestinian president Mahmoud Abbas has told the United Nations that he is keen to reach a peace deal with Israel within a year.
However he also said in his address to the General Assembly on Saturday that Israel must choose between the continuation of settlements and peace.
However, the Palestinians say they will stop unless Israel extends a moratorium on settlement building in the West Bank, due to expire on Sunday.
While Mr Abbas affirmed Palestinian willingness to co-operate with US President Barack Obama's efforts to keep the peace process on track, he went on to list list Palestinian grievances against the Israelis.
These included the blockade of the Gaza Strip and the imprisonment of thousands of Palestinians in Israeli jails.