Earlier this week, they made a successful push towards a strategic pass at the border with Pakistan, capturing a large police base in Badakhshan province in the northeastern corner of the mountainous country.
Most foreign forces withdrew from Afghanistan in 2014, leaving Afghan forces to fight the resilient insurgency with only limited coalition support.
The Taliban fought Afghan forces for two days in Sar-e-Pol province before capturing the district of Kohestanat on Monday evening, the police chief said.
"We asked for air support but did not receive it, so our security forces quit," Asif Jabarkhel said, adding that one policeman and two local fighters were killed in the battle.
Police planned to retake the district, he said. In Kunduz, the Taliban have seized around 70 villages in Khanabad district this week, a spokesperson for the provincial governor said.
More than half the province is now under Taliban control, according to local officials.
They captured two Kunduz districts in June, one of which was quickly retaken by Afghan forces but the other remains under insurgent control.
The militant group was ousted from power by a US-led coalition in 2001.
Most of the US forces left the country last year, but a small contingent of several thousand counter-terror troops remains engaged in combat operations. NATO also runs a separate two-year training mission that will continue through 2016.
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