The Taliban has laid siege to several districts in the northern Afghan province of Kunduz, which briefly fell to the militants last year.
Heavy clashes between Afghan security forces and Taliban militants were reported in the districts of Dasht-e Archi and Qalai-e Zal on July 20.
In Dasht-e Archi, located northeast of the city of Kunduz, the provincial capital, local officials said the Taliban had taken control of most of the district.
Local officials also said most of Qalai-e Zal was under Taliban control after four days of intense fighting.
Kunduz lawmaker Abdullah Qarluq told the AP news agency that the militants had taken complete control of Qalai-e Zal "and also 98 percent of Dasht-e Archi."
Mahmood Danish, a provincial spokesman, denied any district had fallen and said air strikes were ordered in and have helped repel some of the militants.
Last year, the Taliban briefly captured Kunduz city, the first major urban center the militants had seized since the U.S.-led invasion toppled the Taliban in 2001.