According to the Afghan government, the Taliban launched the attack on the city of Pul-i-Khumri in Baghlan at around 5 p.m. (12:30 GMT) on Saturday, simultaneously to while the group was fighting against government forces nearby in Kunduz.
The Afghan Interior Ministry's spokesman, Nusrat Rahimi, said that the situation was under control.
"The situation is under control in Pul-i-Khumri," Rahimi told Sputnik, adding that the Taliban had attacked two districts of the city and that government forces were retaliating.
Rahimi also said that so far three Taliban militants had been killed and two were arrested, adding that no casualties had been reported from the Afghan forces' side.
On Saturday, the Taliban launched an attack on the northern city of Kunduz. However, the government forces regained control of the city, killing at least 35 Taliban militants in the process.
Conflict-struck Afghanistan has been long torn by fighting between government troops and the Taliban, who are currently negotiating a peace deal with the United States.