Since launching the operations on Friday, several villages have also been recaptured from the insurgents, army spokesman in the northern region Mohammad Hanif Rezai said.
The operations, backed by fighting aircraft, would continue until the area is cleansed of the armed militants, the official added, Xinhua reported.
However, Rezai did not say if there were casualties on the security personnel.
The Taliban have yet to make comment.
Both the Taliban and government forces have stepped up operations since the beginning of talks between the United States and the Taliban in Qatar last November.