This is third district in Badakhshan to have been retaken from Taliban in one week, after Warduj and Yamgan districts.
Taliban suffered heavy casualties in the operation to retake Kuran wa Munjan district, the statement said.
The country’s national flag was flying over the district, it said.
Kuran wa Mujan had fallen to Taliban nearly two months ago. The district is popular for having lapis lazuli mineral deposit.