Zabihullah Mujahid said on Twitter that the Islamist movement captured the capital of Takhar and gained control over all the vital buildings.
The Afghan TOLOnews broadcaster, in turn, reported that key districts of Taleqan were under the control of the Taliban, citing sources.
Earlier in the day, the movement said they fully took over the Kunduz and Sar-e Pol provinces in northern Afghanistan, which the Afghan government denied.
The standoff between the Afghan government and the Taliban has flared up amid the pullout of the international forces from the war-torn country. The Taliban have radically ramped up their territorial advances recently, which causes concern by the international community.
*A terrorist organisation banned in Russia and many other countries.