KABUL—As Afghanistan’s armed forces cede and regain ground in the searing summer offensive against the Taliban, they are losing a propaganda war that is affecting the morale of a fearful population waiting for reassurance that the insurgents won’t overrun their country.

Over the weekend, Taliban militiamen stormed districts in the north of the country, furthering the widespread perception that the insurgents are winning against a government that lacks strategy and leadership. Since May 1, the Taliban have stormed 60 districts, with active fighting now going on in some 64 percent of Afghanistan’s territory, according to the Institute of War and Peace Studies, though eight districts have been retaken by Afghan forces. Security sources said that Afghan forces often retreat in order to save civilian lives.