Five other army soldiers were wounded.
One soldier was killed and other wounded at about 9:00 pm local time in Muqor district of the province after the Taliban attacked military check post, according to the statement.
The second attack happened about 3:00 am early Tuesday after the insurgents attacked another military check post in Nani village of Andar district, it said.
The statement said that the insurgents also suffered casualties but there is no exact information.
The statement did not provide further details of the clashes.