The source told Sputnik that the Taliban attacked a military checkpoint in the province's Aliabad district on Saturday night.
The Kunduz governor's office confirmed the incident but declined to comment on the casualties.
On Sunday morning, one policeman was killed and two others suffered injuries in a bomb attack on a security outpost in Khogyani district of Nangarhar province.
According to officials, it was a suicide attack on the checkpoint, ANI reported.
Afghanistan has witnessed a sharp rise in violence. Attacks on security personnel have also escalated.
Data from the Afghanistan Independent Human Rights Commission shows that in 2020, over 2,000 people were killed in incidents for which no one claimed responsibility.
Moreover, the US-Taliban deal, signed in Doha last year that calls for the full withdrawal of US forces from Afghanistan by the end of May, has resulted in an increase in violence.