The conditions of President Hamid Karzai “are very clear, very established, and, certainly, we support them as we did in Iraq, as the U.K. did in Northern Ireland; this is how you end these kinds of insurgencies,” General Petraeus said, referring to the conditions among others that the Taliban respect the country’s Constitution and lay down arms.

He added that any strategy had to be comprehensive and also include traditional elements of counterinsurgency strategy, like training Afghan security forces, and also “coming to grips with the situation in which there are sanctuaries for the insurgents outside the borders of the country in which we are located, and it involves, in a sense, a war of words, of information.”

American support for the process is in part a recognition that “Oh, by the way, you are not going to kill or capture your way out of an industrial-strength insurgency,” General Petraeus said, underscoring the scale of Taliban activity.

The talks are continuous, according to people knowledgeable about them.

General Petraeus’s embrace of talks comes at a difficult moment in the war and at a time when many politicians in the United States are searching for a way to bring the troops home as soon as possible. Popular support has ebbed amid a steady drumbeat of reports documenting the Taliban’s persistence despite the killing of large numbers.

Although on its face a peace deal with the Taliban appears to be a necessary ingredient for the withdrawal of international troops, a reconciliation with the insurgents is also so controversial among many Afghans that the United States is in a delicate position in supporting it. At this point it seems there is an acknowledgment that it would not be possible to win against an insurgency of this scale and that a peace deal might be a major part of any exit strategy.