Israel's prime minister has briefed his cabinet on a package of incentives the US has proposed if it renews a partial freeze on settlement construction.
Washington has reportedly said it will strengthen its commitment to oppose UN resolutions critical of Israel, and offer defence and security guarantees.
In return, Israel would stop building for 90 days in the occupied West Bank.
US President Barack Obama said that Israel's review of the proposal was a "promising" sign.
However, the Palestinian Authority reacted negatively to the proposal because the halt would not include East Jerusalem.
The settlement row has derailed US-brokered direct peace talks, which resumed in September after almost 20 months and broke down only weeks later, when the previous construction freeze expired.
Israel has occupied the West Bank, including East Jerusalem, since 1967, settling close to 500,000 Jews in more than 100 settlements. They are considered illegal under international law, although Israel disputes this.
There are about 2.5 million Palestinians living in the West Bank.
Israel's government was split over whether to accept the new US offer when it was presented by Prime Minister Benjamin Netanyahu on Sunday, according to reports in the Israeli media.
Some ministers are said to have requested further reassurances from Washington, while Vice Premier Moshe Yaalon called it a "honey trap".
"[It] will lead us down a slippery slope and into another crisis with the American administration after three months, or perhaps even sooner," he was quoted as saying by the Haaretz newspaper.
Mr Yaalon was reportedly one of four members of Mr Netanyahu's Likud party who opposed the deal, which would see Israel halt all new projects started since 26 September, when the previous freeze ended.
But the prime minister said the proposal was "not yet final".
"It is still in process of formulation by our and US teams. If and when the formulation is completed, I will bring it up in the appropriate government forum," he explained.
"In any event, I insist that any proposal provides an answer to the State of Israel's security needs both in the immediate range and against threats Israel will face in the coming decade."
According to diplomats, the US has said it will not ask Israel to extend the new freeze when it expires, provide 20 F-35 fighter jets worth $3bn, veto or oppose any initiatives at the UN Security Council critical of Israel, and sign a comprehensive security agreement with Israel at the same time as any peace deal is finalised.
Mr Obama welcomed Israel's approach to the proposal.
"I commend Prime Minister Netanyahu for taking, I think, a very constructive step," he said.
The BBC's Kim Ghattas in Washington says the deal was discussed when US Secretary of State Hillary Clinton met Mr Netanyahu on Thursday.
The Palestinian Authority - backed by the Arab League - has pledged not to return to the talks without a full settlement construction freeze, but have given US negotiators until early November to try to break the impasse.
Washington has been trying desperately for two months to revive deadlocked peace talks, and a 90-day freeze may be enough to get the Palestinians back to the negotiating table, our correspondent says.
Within those three months officials hope to get serious discussions under way about the borders of a future Palestinian state, she adds.
Last month, Mr Netanyahu offered to renew the freeze if the Palestinian Authority recognised Israel as a Jewish state, but it dismissed the idea.
Palestinian officials have argued in the past that recognising Israel as a Jewish state would compromise the rights of 20% of the Israeli population that is not Jewish, and cancel the right of Palestinian refugees to return.