President Obama had hoped to go to his first United Nations meeting next week with at least one diplomatic coup: a plan to restart the long-stalled Middle East peace talks, to be announced in a three-way meeting with the leaders of Israel and the Palestinian Authority.

But after a fruitless week of shuttle diplomacy, his special envoy, George J. Mitchell, returned to the United States on Friday night without an agreement on freezing construction of Jewish settlements and amid fresh signs of differences on the basis for peace negotiations. Mr. Obama now faces the prospect of a meeting with Benjamin Netanyahu, the Israeli prime minister, and Mahmoud Abbas, the Palestinian president, that some say will be little more than a photo opportunity, one that will only underscore how elusive an Arab-Israeli peace agreement is.

The failure of Mr. Mitchell to nail down an agreement with Israel on freezing settlements, which the administration views as vital for successful talks, does not mean that Mr. Obama will not ultimately succeed. Some experts predict that Mr. Netanyahu, a shrewd negotiator, will strike a deal directly with the president, though that seems unlikely to happen before world leaders gather Wednesday for the United Nations General Assembly.

But Mr. Mitchell’s travails — he also faces resistance from Arab countries in making diplomatic gestures toward Israel — show that on yet another front Mr. Obama’s policy of engagement is proving to be a hard sell. If an agreement just to start talking is out of reach, hammering out the details of a comprehensive peace deal seems all the more daunting.

During his weeklong visit to the Middle East, people briefed on the talks said, Mr. Mitchell, the former Senate majority leader, found substantial differences between the sides, even on issues that had been agreed upon in previous negotiations, like the basic configuration of Israel’s borders and whether the status of Jerusalem should be included in peace talks.

The State Department declined to comment on the details of Mr. Mitchell’s discussions, though a spokesman, Ian C. Kelly, acknowledged that the trip had failed to produce a breakthrough.

“Of course we hoped to have an agreement,” Mr. Kelly said. “Of course we were hoping for some kind of breakthrough. But this is going to be — again, it’s going to be — it’s going to demand a lot of patience. And the U.S. is ready to stay patient and stay engaged.”

Other senior administration officials say they do not view their inability to announce a new round of talks next week as a setback. They say that Mr. Obama expected this to be a lengthy, grueling process, and that Mr. Mitchell has already moved Mr. Netanyahu a long way toward accepting some form of freeze and Arab countries toward considering conciliatory measures toward Israel.

“Given the situation we confronted in January 2009, the amount of progress Senator Mitchell has made in nine months is remarkable,” said a White House spokesman, Tommy Vietor.

In a speech Friday at the Brookings Institution, Secretary of State Hillary Rodham Clinton said, “I can guarantee you that President Obama and I are very patient and very determined.”

Still, it was telling that in listing the Obama administration’s priorities for the General Assembly, Mrs. Clinton did not even mention the Middle East, focusing instead on nuclear nonproliferation, Iran, Iraq, Afghanistan and Pakistan, among other issues. She mentioned the need for a “comprehensive peace between Israel and the Palestinians” at the end of a wide-ranging address.