Israeli and Palestinian negotiators cleared the first hurdle on Thursday in their elusive quest for Middle East peace: they agreed to keep talking, two weeks from now in Egypt.

But on a richly choreographed day of diplomacy, filled with solemn promises to tackle the tough issues dividing them, the Israeli and Palestinian leaders did not confront the one issue that could sink these talks in three weeks: whether Prime Minister Benjamin Netanyahu will extend a moratorium on the construction of Jewish settlements in the West Bank.

The Palestinian Authority president, Mahmoud Abbas, has threatened to walk out of the negotiations if Israel does not extend the moratorium beyond September. But officials said the two leaders barely broached the topic during three hours of talks, which covered the gamut of issues that have divided Israel and the Palestinians for decades.

Instead, Mr. Netanyahu and Mr. Abbas focused on mechanics, agreeing to aim for a “framework agreement” that resolves the core issues in carving out a Palestinian state from the Israeli-occupied territory on the West Bank. The fine points of a treaty would be worked out after that.

In a sign that the Obama administration will continue to play a visible role in the process, Secretary of State Hillary Rodham Clinton and the administration’s special envoy for Arab-Israeli affairs, George J. Mitchell, will take part in the next meeting, likely to be in the Red Sea resort of Sharm el Sheik.

Mrs. Clinton, in formally reopening the negotiations at the State Department on Thursday morning, acknowledged, “We’ve been here before, and we know how difficult the road ahead will be.” But she expressed confidence that the core disputes separating the two sides could be resolved within a year.

Analysts said they were encouraged by the goal of a “framework agreement,” which could be a practical vehicle for both sides to resolve vexing “final status” issues: borders, security, the political status of Jerusalem, settlements and the rights of Palestinian refugees.

“They’ve set for themselves an achievable objective in a one-year time frame,” said Martin S. Indyk, a former American ambassador to Israel and Middle East peace negotiator. “A comprehensive agreement would have been unrealistic with that kind of timetable.”

Mr. Netanyahu and Mr. Abbas met alone for 90 minutes in Mrs. Clinton’s office and emerged smiling, officials said. After two years without a face-to-face meeting, the two spent some time breaking the ice.

Mr. Abbas brought Mr. Netanyahu up to date on how far he had gotten in his talks with former Prime Minister Ehud Olmert of Israel. Palestinian negotiators are hoping to use the concessions Mr. Olmert made — which have never been publicly acknowledged by Israel — as a basis from which to start these negotiations. But Mr. Netanyahu has so far balked at that.

“The climate, and atmosphere, was positive and serious and down to business,” said Nabil Shaath, foreign relations commissioner of Mr. Abbas’s Fatah Party, who is negotiating for the Palestinians.

“But the cloud is still there,” he added. “The Israelis gave absolutely no hopeful signs that they will continue the moratorium. And in our point of view, that is the litmus test for the Israelis.”

On Wednesday, officials said, President Obama spoke bluntly to Mr. Netanyahu and Mr. Abbas at the White House, urging them not to allow the impasse to scotch the talks. But Mr. Netanyahu has not offered any hint of a compromise, and analysts say he is hemmed in by his right-leaning coalition, which could splinter if he simply extended the moratorium.

The more likely outcome, officials said, is a compromise in which Israel would agree to limit settlements, but exempt West Bank areas that are certain to remain part of Israel under a peace deal. It could also offer a limited extension, based on agreeing on the borders of a Palestinian state.

Israeli officials declined to discuss the issue of settlements but said the overall tenor of the talks was “good and constructive.” Citing the killings of four Israeli settlers in the West Bank this week, Mr. Netanyahu said security would have to be a critical theme of the talks. He said that the rise of Iran, and its support of militant groups, had radically altered the landscape for peace talks.

“There is a commitment on our part to address all issues,” said Jonathan Peled, the spokesman for the Israeli Embassy in Washington. “A lot will depend on addressing Israel’s security concerns, and whether the Palestinian leadership is willing to make historic compromises.”

It was a day of self-conscious history-making at the State Department. Just before 10 a.m., the Palestinian delegation entered the ornate Benjamin Franklin Room. Twenty minutes later, the Israelis entered, taking their seats and gazing at the Palestinians across a rose-colored carpet.

“I fervently believe that the two men sitting on either side of me, that you are the leaders who can make this long-cherished dream a reality,” Mrs. Clinton said, gesturing to Mr. Netanyahu and Mr. Abbas.

Mrs. Clinton paid tribute to the diplomats in the room, several of whom she noted were veterans of the process. Watching from behind was Dennis B. Ross, a senior White House adviser on the Middle East who helped run the Camp David negotiation for Mrs. Clinton’s husband, President Bill Clinton, in 2000. Also at the table were seasoned negotiators like Mr. Netanyahu’s key adviser on the process, Yitzhak Molcho, and Mr. Abbas’s chief negotiator, Saeb Erekat.

“The people sitting here have worked very hard for many years,” she said. “Now it’s time to get to work.”

But Mrs. Clinton also repeated the oblique criticism of Arab states voiced by Mr. Obama on Wednesday. “We hear often from those voices in the region who insist this is a top priority and yet do very little to support the work that would actually bring about a Palestinian state,” she said.

Saudi Arabia and other Persian Gulf states have been slow to deliver promised financial aid to the Palestinian Authority, officials close to Mr. Abbas said, and the authority faces an increasingly dire shortfall.

Mrs. Clinton also addressed the people of the Middle East directly. “Your leaders may be sitting at the negotiating table,” she said, “but you are ultimately the ones who will ultimately decide the future.” Mrs. Clinton asked Israelis and Palestinians for their “support and patience” in the process.

On Friday morning, she is to give an unusual joint interview to Israeli and Palestinian television channels, part of what will be an aggressive strategy to sell the peace process at home and abroad.