The incident was confirmed by army spokesman in the northern region, Mohammad Hanif Rezai.
Dozens of militants were also injured in the operations backed by fighting aircraft which covered the restive Charbolak and Sholgara districts.
According to Rezai, several villages have been liberated so far from the clutches of the armed militants.
However, Taliban militants, who were active in parts of Balkh province with Mazar-e-Sharif as its capital, 305 km north of Kabul, have yet to make any comment.
Earlier this year, during the holy month of Ramadan, a Taliban attack killed 25 soldiers in the western part of the country.
The incident occurred when the Taliban assaulted a military check post in the western Farah province bordering Iran.
However, the deputy chairman of the provincial assembly, Shah Mehmood Naimi, told Anadolu Agency that scores of Taliban insurgents stormed a military compound in an overnight attack on the main highway linking Herat and Kandahar provinces.