Israeli Defence Minister Ehud Barak has told the BBC there is a "50-50" chance of reaching a deal with Palestinians about Israel's settlement moratorium as a 10-month partial ban winds down.
Palestinians have said they could leave recently resumed peace talks if the construction freeze is not extended.
West Bank settlers are preparing to resume building if no deal is reached.
Mr Barak is returning home from the UN in New York, where he has been leading Israel's negotiating team.
Israel says the settlements are no bar to talks, but US negotiators have been working intensively to secure a deal.
Speaking exclusively to the BBC's diplomatic correspondent Bridget Kendall, 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.
"I think the chance of achieving a mutual agreed understanding about the moratorium is 50/50," he told the BBC. "I think the chances of having a peace process is much higher."
"I hope it will not be blocked by this moratorium issue and that we will sail full engines forwards [to] substantial negotiations and agreement," Mr Barak told the BBC.
In a speech on Saturday to the United Nations General Assembly, Palestinian leader Mahmoud Abbas said Israel must choose between peace and the continuation of Jewish settlements.
Palestinians were willing and ready to reach a comprehensive and just peace agreement with Israel, Mr Abbas told the assembly, declaring that their "wounded hands" carried an olive branch to the Israelis.
But Mr Abbas stopped short of publicly threatening to withdraw from talks with Israel if the moratorium on new West Bank construction is not extended.
In an interview published in the Arabic al-Hayat newspaper on Sunday, Mr Abbas was quoted as saying said if settlement construction resumed he would not call off talks but rather take the issue to a forum of the Arab League.
Despite this, if Mr Abbas flinches first and offers a compromise, for many Palestinians this will reinforce his reputation as a weak leader, says the BBC's Jon Donnison, in the West Bank town of Ramallah.
If he holds his ground and pulls out of the talks he could be portrayed as the spoiler, our correspondent adds.
Israel's 10-month freeze on West Bank settlement-building expires at midnight local time on Sunday (2200 GMT). The moratorium freeze has never applied to East Jerusalem settlements.
It is estimated that about 2,000 housing units in the West Bank already have approval and settler leaders say they plan to resume construction as soon as possible.
"Our policy now is to resume a natural pace of building," said Naftali Bennett, director general of the settlers' organisation, the Yesha council.
They are backed by right-wing politicians including members of the Likud party, headed by Israeli Prime Minister, Benjamin Netanyahu.
On Sunday, Mr Netanyahu's office issued a statement urging settlers and their political leaders to "show restraint and responsibility today and in the future".
One Likud MP, Danny Danon is expected to attend a symbolic ground-breaking ceremony at the settlement of Revava on Sunday.
In recent weeks, settlers there have erected new temporary homes on the hillside overlooking the Palestinian village, Deir Istiya, angering local people.
"The most crucial thing is settlements, for me and the majority of Palestinians," says mayor of Deir Istiya, Nazmi Salman. "All Palestinians know [there will be] no peace with settlements."
Correspondents say any resumption of construction is likely to be small in scale, as most projects will require approval from Israel's defence ministry.
On Thursday, US President Barack Obama urged Israel to extend its moratorium, saying it had "made a difference on the ground, and improved the atmosphere for talks".
Nearly half a million Jews live in more than 100 settlements built since Israel's 1967 occupation of the West Bank and East Jerusalem. They are held to be illegal under international law, although Israel disputes this.