Taliban forces are closing in on the one part of Afghanistan they don’t control: the Panjshir Valley, near the imposing Hindu Kush mountain range north of Kabul. The Islamist group is pressing opposition leaders there to join a new government, threatening a military assault if they don’t.

Politicians in Panjshir—who say they are backed by a militia of several thousand men, bolstered by the remnants of the Afghan army, and with military hardware such as helicopters—say they have rebuffed Taliban overtures, which they say fall short of the promises of autonomy they want.

On Sunday, Taliban and rebel forces skirmished just outside the valley, a resistance leader said. Families of valley residents said the Taliban also cut telephone and internet connections to the valley.

At the same time, talks between the two sides continued, officials in both camps said.

“The problem is that they are unwilling to make any concessions. And we’re unwilling to accept any type of political system that isn’t inclusive,” said Ali Nazary, head of foreign affairs for the rebels, who call themselves the National Resistance Front.