Netanyahu said details of the proposal were still being hammered out, but he has promised to put the final draft to his 15-member security cabinet for approval.
Late on Sunday, a political source said Netanyahu had not agreed on the exact terms of the freeze and was "holding out" over a number of conditions.
"Only when these conditions are accepted will there be an understanding about the subject and the issue will be brought for the cabinet's approval," he said.
On Monday, US Secretary of State Hillary Clinton underlined Obama's support, saying Netanyahu was making a "serious effort" in considering the American proposal.
"We are in very close touch with both the Israelis and the Palestinians, working intensively to create the conditions for the resumption of the negotiations," she told reporters in Washington.
Palestinian president Mahmud Abbas had been due to receive a briefing on the proposals on Monday from David Hale, assistant to US Middle East envoy George Mitchell, but he postponed it as the Muslim holiday of Eid al-Adha loomed.
Although Netanyahu faces an uphill battle to garner support for the plan, press reports suggested he was likely to get the proposal through the security cabinet with a wafer-thin majority of seven to six, with two abstentions.
The mainstream Israeli papers seemed to agree that Netanyahu can count on the support of three ministers from his Likud party, two Labour members including Defence Minister Ehud Barak, and an independent.
Leading the opposition is Foreign Minister Avigdor Lieberman with two others from his ultra-nationalist Yisrael Beitenu party, and three Likud hardliners.
Two ministers from the ultra-Orthodox Shas party have agreed to abstain.
Washington's aim is to bring Abbas back to the negotiating table so the two parties can begin discussing borders, a Haaretz editorial said.
"At the heart of the American proposal is the demand to demarcate the borders of the Palestinian state that Netanyahu has promised to see established," it said.
"Setting the border will bring order to the settlement issue and will make it clear where Israel is entitled to build and where it is not."
Intelligence Minister Dan Meridor, a security cabinet member who supports extending the freeze, told Haaretz it was "imperative" that Israel approve the US plan.
"The freeze is not the main thing, rather the negotiations which are an Israeli interest of the top order," he said.
"Israel has an interest in creating a border, with Israel on the one side and the Palestinian state on the other."
Until now, Netanyahu has avoided all talk of borders, an issue of great concern for hardliners within his cabinet.
Barak told Israel's army radio from Paris that US officials had asked Israel to discuss borders, but that there was no fixed timetable.
"The Americans expect us, and rightfully so, to seriously discuss all the core issues as soon as we begin," he said.
"They are unable, and do not intend, to dictate to us that by the sixth day we have to resolve the issue of borders, and by the ninth day the issue of refugees."
Peace talks, which began two months ago, shuddered to a halt over renewed settlement activity following the end of a 10-month building freeze, with the Palestinians refusing to return to the table without a new moratorium.
The Palestinians say they will accept only a "comprehensive" ban on all settlement construction, including in annexed Arab east Jerusalem which they want for a future state.
"If Netanyahu stops the settlements, we will go back to direct negotiations," chief Palestinian negotiator Saeb Erakat told AFP on Monday.
The proposed freeze would not apply to east Jerusalem.