Much of the work done by American Special Operations forces in Afghanistan or anywhere else is highly classified, and information about it is closely guarded. A senior American military officer, for instance, said he did not know whether such forces were based in Maidan Wardak or were based elsewhere and were flown in for missions.

Afghan officials are, for the most part, told even less, and many in the Karzai administration no longer wish to allow Americans to continue “running roughshod all around our country,” said a person who is close to Mr. Karzai.

As additional evidence of that sentiment, the person close to Mr. Karzai, who asked not to be identified because he was discussing internal deliberations, cited an order issued earlier this month by Mr. Karzai sharply curtailing the circumstances in which Afghan forces could call in coalition airstrikes.

That order, however, simply brought Afghan forces into line with the rules that coalition troops have followed since last year. Neither Afghan nor foreign military commanders believe its impact will be far-reaching.

Image Maidan Wardak is seen as a crucial area in defending the capital against the Taliban. Credit... The New York Times

It will probably be harder to assess the effects of the ban decreed on Sunday, and the competing views on the matter illustrate just how far apart Afghan and coalition officials are when it comes to charting a course for the war.

With the withdrawal of American forces picking up pace, most of the coalition’s conventional forces in eastern Afghanistan, including in Maidan Wardak, have shifted into advisory roles. Among coalition troops, offensive operations are increasingly becoming the sole purview of the Special Operations forces.