The 209th Shaheen Corps of the Afghan army in a statement said three Taliban insurgents including a commander of the Red Unit of the group were killed during the clash with the Afghan forces.
The statement further added that the Taliban commander killed during the clash has been identified as Mumtaz and at least three others were critically wounded.
According to the Shaheen Corps, the clash took place in the vicinity of Chel Cheragh Bagh Sherkat area of the province.
The anti-government armed militant groups including the Taliban insurgents have not commented regarding the report so far.
Kunduz is among the relatively volatile provinces in North of Afghanistan where the Taliban insurgents are actively operating in some of its districts and often carry out insurgency activities.
At least eighteen militants were killed during the operations of the Afghan armed forces in this province last week.
The ministry of defense said last week that the operations were conducted with the close air support of the Afghan Air Force in Chahar Dara district.
According to the defense ministry, five militants were also wounded and three others were arrested during the same operations.
The Afghan security forces also destroyed a vehicle and seven improvised explosive devices during the operations while some weapons and ammunition were confiscated, MoD said.