As the Palestinians consider withdrawing from peace talks with Israel unless a freeze on Jewish settlement building in the West Bank is extended, Prime Minister Benjamin Netanyahu of Israel is engaged in his own calculations about whether accepting an American offer aimed at prolonging the freeze would destroy his political coalition.

Mr. Netanyahu is examining an American offer of a 60-day freeze extension in exchange for security and political guarantees. A deadline looms this weekend, since the Arab League is gathering in Libya on Friday to discuss the Palestinians’ request for guidance on what to do next.

Mahmoud Abbas, the Palestinian Authority president, has said that he could not continue in the month-old talks if settlement building started up again. The Arab leaders seem likely to agree with him. But Mr. Netanyahu said that the freeze was a one-time gesture and that he was not inclined to extend it.

The pressures on him to go in one direction or the other have been strong. The settler movement has been running advertisements warning that the freeze would be extended and calling that a betrayal of Mr. Netanyahu’s promise. They have urged smaller right-wing religious parties in his coalition to leave the government if that occurs.

On the other side, Mr. Netanyahu’s Labor partners, the only left-leaning members of the government, say they will drop out of the coalition if the talks fall apart over the settlement issue.

“If they destroy the peace talks over this minor issue of settlement building, the Labor Party will leave the government,” Minorities Affairs Minister Avishay Braverman of Labor said in a telephone interview. “The long-term viability of Israel depends on dividing the territory of the Holy Land.”

On Tuesday, another Labor Party official, Isaac Herzog, the minister of welfare, visited King Abdullah II of Jordan and said afterward by telephone that “everyone on all sides understands we need to seize the moment for peace, but we have become stuck on this settlement issue.”

“There is a big effort being made to overcome it, and I believe a compromise will be reached,” Mr. Herzog said.

Mr. Netanyahu met with his six top ministers on Tuesday, but a statement from his office said that the Palestinian question had not been on the agenda. On Monday, Mr. Netanyahu announced that negotiations with the United States were at a delicate phase and that he would not be commenting publicly because discretion was required. The ministers may have decided to keep their talks entirely secret.

The seven, who call themselves the “septet” or “forum of seven” (counting the prime minister) represent the divided Israeli political map on this topic. A majority would have to favor a freeze extension for it to occur, and whether such a majority exists is unclear. The septet is an advisory body without statutory power, but once it comes to a decision, its influence is strong.

The so-called security cabinet of 15 members or the full cabinet of 30, both of which do have statutory powers, would very likely follow suit. It is not clear when any of these ministerial groups are likely to meet specifically on this issue. It could be before the Arab League meeting or even just after it.

Most of the handicapping says that of the seven, three would favor the 60-day extension urged by the United States — Defense Minister Ehud Barak of Labor, Intelligence Minister Dan Meridor of Likud and Mr. Netanyahu himself — while those clearly opposed are Foreign Minister Avigdor Lieberman of Yisrael Beiteinu, himself a settler, and Eli Yishai of Shas.

That leaves two Likud hard-liners — Moshe Yaalon, the minister of strategic affairs, and Benny Begin, a minister without portfolio.

All seven agreed to the 10-month freeze last November. Mr. Begin and Mr. Yaalon have said that it should not be extended. Reached by telephone on Tuesday, Mr. Begin said that was indeed his view. Told that ending one freeze would not necessarily bar a second shorter freeze, he said, “What you say is logical, but I cannot comment on it.”

To govern, Mr. Netanyahu needs a parliamentary majority. Israel’s Parliament consists of 120 members, so a coalition requires 61 seats. Mr. Netanyahu has a very comfortable governing coalition of 74 seats. It is made up of his own right-leaning Likud party, the ultranationalist Yisrael Beiteinu party of Mr. Lieberman, the left-leaning Labor Party of Mr. Barak, the rightist religious party Shas of Mr. Yishai and two smaller parties also of the religious right, Habayit Hayehudi and United Torah Judaism.

In theory, he could jettison his far-right partners and bring in the large center-left opposition party, Kadima, led by Tzipi Livni, which favors the peace talks and a Palestinian state. But at the moment neither Mr. Netanyahu nor Ms. Livni seems to want to move in that direction. Ms. Livni is seen as hoping the government will collapse and new elections will bring her to power.

There is little evidence of that happening soon. Still, tensions have increased within the coalition over the Palestinian issue, particularly over the settlement building extension. Labor ministers have expressed outrage over Mr. Lieberman’s speech at the United Nations last month in which he said that no peace could be expected for decades.