With a critical deadline looming, Israelis and Palestinians were searching on Friday for a compromise that would rescue newly resumed peace talks from foundering over an old Mideast grievance- Israeli settlement construction.

Israel’s 10—month slowdown on settlement building expires on Sunday, and Prime Minister Benjamin Netanyahu has rebuffed Palestinian and U.S. calls for an extension. With Palestinian President Mahmoud Abbas having threatened to walk out of talks if construction resumes at full force, the U.S. is trying to wrest concessions from both sides to keep negotiations from breaking down just three weeks after they began.

Mr. Netanyahu ordered his special envoy to the negotiations, Yitzhak Molcho, to remain in the United States for further discussions, while Mr. Abbas and his leading advisers were also in the U.S. meeting with American officials.

Mr. Netanyahu has signalled a willingness to seek a way out of the impasse, saying earlier this month that the current restrictions on settlements will not remain in place, though there will still be some limits on construction.

An Israeli official said on Friday that “all the proposed building for the coming year would in ... no way change the parameters for such a historic peace treaty.”

“The sort of building that’s being considered is minor and in no way seriously changes the current realities on the ground,” he said, without offering specifics. He spoke on condition of anonymity because the search for a compromise was still in progress.

The West Bank settlements that are a major source of contention between the two sides are home to 300,000 Jewish settlers and eat up land the Palestinians want for their future state. Some 180,000 more Jews live in east Jerusalem, the sector of the city that the Palestinians hope to establish as their capital.

The Palestinians hope to win a total freeze on any new construction in the coming months. While Mr. Abbas has demanded an extension as a condition for continuing talks, there have been signs he has softened his position.

The tense political climate has added to the volatility in the contested holy city, where the killing of a Palestinian man by a Jewish security guard sparked rioting earlier this week.

With a major Jewish holiday coinciding with weekly Muslim prayers on Friday, Israeli authorities deployed a reinforced contingent of thousands of police in and around east Jerusalem as a precautionary measure, and limited entry to Muslim worshippers.

With no diplomatic breakthrough in the offing, the U.S. has plunged directly into the settlement construction fray threatening to derail the talks, offering proposals to keep alive what it sees as a now—or—never effort to end decades of bloodshed.

“There is significant back and forth going on,” U.S. State Department spokesman P.J. Crowley said late Thursday. U.S. officials were “reminding them (the parties) of their responsibilities” not to do anything to jeopardize the talks, he added.

The new surge of diplomatic activism reflected President Barack Obama’s impassioned appeal to the world at the United Nations on Thursday to help Israelis and Palestinians resolve their decades—old conflict.

Under intense U.S. pressure, Mr. Netanyahu agreed in November to limit construction in the West Bank in a bid to coax the Palestinians back to the negotiating table. A de facto freeze has been in place in east Jerusalem as well.

Mr. Netanyahu, a hard—liner who only recently became a convert to the notion of a Palestinian state, has balked at extending the curbs on West Bank construction beyond Sunday, saying that would fracture his pro—settlement coalition government.

Meanwhile, Palestinian health officials said that a Gaza fisherman was killed by Israeli naval fire. The Israeli military said a fishing boat strayed from the limits Israel has prescribed and was fired upon after ignoring warning shots.

Also, Mohammed Dababish, a senior Hamas security official arrested in Egypt on suspicion of posing a threat to Egyptian security, has been released and was en route to his home in Gaza, Hamas and Egyptian officials said.

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