Mr. Ali has extensive experience fighting against Al Qaeda in the area but has also been accused of having helped Bin Laden escape from Tora Bora in December 2001, reportedly betraying his American and Afghan allies as they closed in on the Qaeda leadership.

Mr. Ali has denied having done so.

The Islamic State in Khorasan, as the militants in Afghanistan and Pakistan are known, has no direct connection with Al Qaeda, which is largely a spent force in the area. But the Islamic State was originally formed by Qaeda elements, and the two groups have many doctrinal similarities.

Government forces and their coalition allies in the Tora Bora area have engaged in little recent fighting against the Taliban who have been entrenched there, supported by local tribes along the mountainous border with Pakistan. But since March, Afghan forces supported by American Special Operations troops have been mounting a vigorous campaign against the Islamic State in Achin District, also in the Spin Ghar range but about 50 miles to the east of Tora Bora.

All six of the American soldiers killed in Afghanistan so far this year died in the fighting around Achin District.

The American military said it had killed hundreds of Islamic State fighters in the Achin District area, including the “emir” of the Islamic State in Khorasan, Sheikh Abdul Hasib. Mr. Hasib was a former commander with the Pakistani Taliban, who broke away to join the Islamic State. The Islamic State and the Taliban have been competing savagely for dominance in the areas they control, but the more extreme Islamic State fighters have dominated Achin District as well as some other areas in southern parts of Nangarhar Province.

Taliban officials are concerned about the Islamic State’s appeal to younger fighters impatient with the progress of the 15-year insurgency.

In the Tora Bora area, residents were angry at both the Taliban and the government for allowing the Islamic State to take over. Malak Tor, a tribal elder from Pachir Agam District, where Tora Bora is situated, complained that residents’ demands that the government mount an offensive to protect Tora Bora were ignored.