People said that it is not possible to fire on U.S. forces,” said Muslim Mohabat, a former Taliban fighter from Watapor District in Kunar Province. “They would say the barrel of the rifle would bend if you open fire on them, but we attacked them, and nothing happened.”

“Then we kept attacking them and forced them to leave the valley,” said Mr. Mohabat, who fought in some of the most violent battles of the war with the United States.

In the insurgents’ view, their advances will inexorably lead to the end of the Kabul government.

“On the battlefield there is a sense that, ‘We’re stronger than ever,’’’ said Ashley Jackson, a Taliban expert at the Overseas Development Institute. “Power-sharing and democracy, these are anathema to their political culture.”

Fahim Abed, Fatima Faizi and Thomas Gibbons-Neff contributed reporting.

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