"The operations were conducted in Herat, Khost, Maidan Wardak, Helmand, Sar-e-Pul, Kunduz, Takhar, Faryab and Jowzjan provinces, as a result 19 armed Taliban members were killed and one was arrested by Afghan National Security Forces," the ministry said on its website.
The ministry also said that Afghan National Police had confiscated light and heavy rounds of ammunition, as well as 1,700 kilograms (more than 3,700 lbs) of improvised explosive devices (IED).
The police also defused two rockets and three IEDs in the Kabul and Faryab provinces.
The Taliban is an insurgent group operating in Afghanistan and Pakistan. The militants are known to carry out attacks on authorities and civilians, seeking to enforce strict Sharia law.
In 2014, the Taliban intensified its activity in Afghanistan amid the withdrawal of international troops from the country.