JERUSALEM — After nearly two years of frustration and failure, the Obama administration began its Middle East peace efforts anew on Monday with its special envoy, George J. Mitchell, holding talks here on ways to improve the atmosphere between Israel and the Palestinians and ultimately negotiate over the core issues that separate them.

Last week the administration ended its effort to persuade Israel to freeze settlement building in the West Bank as a precursor to direct talks. Instead, there will be no direct talks for now. Rather, Mr. Mitchell will ask both sides to lay out their negotiating positions to the United States separately and the Americans will seek ways to bridge the gaps.

Mr. Mitchell met with Prime Minister Benjamin Netanyahu of Israel on Monday and was due to see President Mahmoud Abbas of the Palestinian Authority in the West Bank on Tuesday. He will then meet with the foreign ministers of the Arab League in Cairo on Wednesday.

Mr. Mitchell, who has not been here for three months, found himself pursuing this more indirect strategy after the Obama administration withdrew an offer to Israel of warplanes and diplomatic assurances in exchange for a 90-day freeze on settlement construction.

Israeli officials say Mr. Netanyahu had accepted the offer in principle but before it was accepted by his government Washington pulled out, worried that it placed too much pressure on those 90 days and that the Palestinians might not negotiate because the proposed freeze excluded East Jerusalem.

At an economic conference in Tel Aviv on Monday, Mr. Netanyahu said that although he had been ready to consider another freeze, he was happy to see the emphasis shift from a construction halt — what he called a marginal issue — to core questions like mutual recognition, security and refugees.

Israeli officials said they expected that initial discussions with the Americans would center on gestures that Israel would offer Palestinians — easing of security, improved economic opportunities — and how to structure the talks ahead.

Mr. Netanyahu and Mr. Abbas did hold direct talks in September near the end of a first settlement construction freeze. But Mr. Abbas ended those talks when the freeze ended, and efforts since then have focused on returning to those direct talks. Now, the initial approach will be limited to each side’s speaking with the United States.

Among the Palestinians, the prevailing atmosphere was one of sourness and gloom. Officials said they did not expect Mr. Mitchell to bear any new ideas or encouraging proposals. They questioned the ability of the United States to play the role of mediator and expressed uncertainty about where to go from here.

After a meeting on Sunday, members of the Fatah Central Committee, the main decision-making body of Mr. Abbas’s party, said they opposed any negotiations with Israel, direct or indirect, in the absence of a settlement freeze. They added that there would have to be clear terms of reference for any further talks, namely a two-state solution based on the 1967 lines.

“Regretfully,” Azzam al-Ahmed, a Fatah Central Committee member told the radio station Voice of Palestine on Monday, “the American administration is still moving in the shadow of the Israeli stance, in order to avoid upsetting the Israeli right-leaning government.”

Khalil Shikaki, a prominent Palestinian political analyst based in the West Bank city of Ramallah, said the Palestinian negotiators would probably continue to engage with the Americans and share their thinking with Washington.

“But the Palestinian side will most likely want to avoid the perception that they are engaged in negotiations with the Israelis,” Mr. Shikaki said in a telephone interview. Putting the emphasis on engagement with the Americans, he continued, would represent a “shift in focus” from the so-called proximity talks, the indirect, American-brokered negotiations that took place earlier this year.

At the same time, the Palestinians are pursuing other options, chiefly seeking international endorsement for the 1967 lines as the borders of their future state.

“There is a growing desire on the part of the Palestinian public to seek out alternative means,” Mr. Shikaki said.