Indicators from the White House, though, have not been as sure. President Obama has yet to decide how many troops might stay on after combat units leave at the end of 2014. Many numbers have been floated, but nothing has been determined.

“At what point does dealing with him become such a political pain that people in Washington, in Congress, say, ‘Let’s rethink the map on this a little bit,’ ” said one Western official in Kabul. “I don’t think Karzai fully understands this — understands the advancement of U.S. feeling on this,” said the official, who spoke on condition of anonymity because of the delicacy of the continuing negotiations.

Many Afghan observers say that Mr. Karzai is trying to keep himself politically potent during the last year of his term by playing to at least three Afghan constituencies: his ethnic Pashtun base; ethnic Tajik and Hazara leaders in his government; and, notably, the Taliban, who have rejected negotiations with him.

In past speeches, Mr. Karzai has sometimes adopted a yearning tone as he has expressed a desire to be the Afghan leader who could unite the country’s factions, including bringing the Taliban in from the battlefield.

And in his recent banning of American commandos from Wardak Province, a Taliban stronghold, some Afghan observers see an attempt to reach out to the insurgents by proving that he has the power to halt military action against them. Others believe he is trying to tap into Afghans’ frustrations with giant foreign military vehicles on their roads, heavily armed foreign soldiers on foot patrols in their fields and night raids on their homes.

But since his words have had only limited effect on the Americans, they increasingly ring hollow to many Afghans. At the same time, the reality on the ground has changed: increasingly, the war is being fought — and in some cases abuses are being carried out — by Afghan forces that are seen as acting in Mr. Karzai’s name despite having been mostly trained by Americans.