But Mr. Mujahid said progress was made on a withdrawal, and he emphasized that the insurgents still wanted to negotiate.

“Since these issues are critical and need comprehensive discussion, it was decided that talks about unsolved matters will resume in similar future meetings,” he added.

The basic outlines of the emerging deal have leaked out through Taliban sources. American officials have been tight-lipped by comparison, though Western diplomats tacitly confirmed those outlines.

The Americans would promise to withdraw their 14,000 troops, and the Taliban would agree to never again allow their territory to be used by extremists like Al Qaeda, the terrorist network that staged the 2001 attacks on the United States from Afghanistan and set off the start of the war.

That much seemed in agreement. But as always, the devil is in the details. How long would the cease-fire be, and would it start before, after or even during the American withdrawal? How long a time frame would the withdrawal cover?

All of these questions are potential deal-breakers.

Taliban sources remained optimistic, even as Western diplomats expressed concern that there would not be a deal from this round of Doha talks. On Saturday afternoon, Sayed Akbar Agha, a former Taliban official who now lives in Kabul but keeps close contacts with insurgent leaders, said he had just spoken to them.

“I have been told that talks are going ahead very well and we are close to an agreement,” he said. Whatever the result this time, Mr. Agha said, “Afghanistan was never so close to peace in these past years. What is happening now has never happened before.”