According to local officials, the Taliban, who have mobilized forces from other areas in Nuristan province, attacked Want Waigal around 9 am local time on Wednesday.
Governor of Want Waigal Rahmatollah Rahmati said Afghan security forces have rushed to the area to ward off the militants and have repulsed several attacks by the militants, but clashes still continue.
Meanwhile, Reuters quoted the Taliban's main spokesman as saying on Wednesday that the militants were close to taking Want Waygal, a day after they took Jani Kheil district in Paktika province, further to the south.
Over the past week, the insurgents have also taken districts in Ghor province in the west and Faryab in the north, although the Afghan Defense Ministry said government forces had retaken Kohistan district in Faryab.
Kunduz, the northern city which the Taliban captured briefly in 2015 and managed to enter in 2016, has also been under heavy pressure.
The Taliban, who ruled the country before being ousted by a US-led invasion in late 2001, have renewed armed insurgency, launching attacks on Afghan military forces.
They have intensified attacks in spring and summer known as the fighting season in the war-torn country.