“We are in Afghanistan for one express purpose: Al Qaeda,” he said. “Al Qaeda exists in those mountains between Afghanistan and Pakistan. We are not there to nation-build. We’re not out there deciding we’re going to turn this into a Jeffersonian democracy and build that country.”

The administration’s shift in thinking is gradual but has been perceptible in the public remarks of various officials. The incoming commander of the military’s Central Command, Gen. James N. Mattis, was asked last week by Senator Jack Reed, Democrat of Rhode Island, whether the administration’s July 2011 date for starting to withdraw American troops implied a shift in emphasis from counterinsurgency to a strategy concentrating on killing terrorists.

“I think that is the approach, Senator,” he replied.

The emerging American model can best be described as “counterterrorism, with some counterinsurgency strategy that forces the hands of insurgent leaders,” said a diplomat with knowledge of the planning. It melds elements of both strategies in a policy that continues to evolve, as conditions change.

Some of the feelers to the Taliban are being put out by the Karzai government and some by the Pakistanis. Some, eventually, will be handled by General Petraeus and other military officials. Contacts are being kept under wraps, several officials said, because any evidence that insurgent leaders are talking to American or Afghan officials could be used against them by rival insurgents.

Another factor that has spurred talk of reconciliation is a classified military report, called “State of the Taliban,” prepared by Task Force 373, a Special Operations team composed of the army’s Delta Force and Navy Seals, which has captured insurgents and taken them to Bagram Air Base for interrogation.

While the report does not offer a silver bullet for how to deal with the Taliban, one official said that for the first time, it gives Americans and their allies “a rich vein of understanding of why the Taliban was fighting and what it would take them to stop.” The report depicts the Taliban as spearheading a fractured insurgency, but one in which conservative Pashtun nationalism and respect for Afghan culture are both at play, this official said.

Despite deep American concerns about Pakistan’s trustworthiness as an ally, Pakistan has also emerged in recent months as a potential agent for reconciliation. Mr. Karzai has held at least two meetings with General Kayani of Pakistan. American officials say they believe that their talks have not yet delved into the details of negotiations with insurgent leaders, but Pakistan is eager to play a role in talks with the Haqqani network, a major insurgent group based in the country that has close ties to its intelligence service.