Video on social media showed a group of Taliban members raising their flag outside the Panjshir provincial governor's compound, with one declaring, "The capital of the Panjshir province is under the control of the Mujahideen."
Panjshir province was the last pocket of armed resistance against the Taliban. It had seen fighting over the weekend with the National Resistance Front of Afghanistan (NRFA), led by Panjshiri leader Ahmad Massoud.
"Panjshir province completely fell to the Islamic Emirate of Afghanistan," the Islamist militant group's spokesman, Zabihullah Mujahid, said in a tweet on Monday (September 6), adding that some enemy fighters had been killed in battle and others had fled.
There was no immediate word from Massoud, who leads a force made up of remnants of regular Afghan army and special forces units as well as local militia fighters.
Ali Maisam Nazary, head of foreign relations at the National Resistance Front of Afghanistan, said the Taliban's claim of victory was false and opposition forces continued to fight.
The Taliban seized control of the rest of Afghanistan three weeks ago, taking power in Kabul on August 15 after the Western-backed government collapsed and President Ashraf Ghani fled the country.