The deadly attacks that claimed the lives of at least 14 policemen come days after the armed group announced conditional amnesty to Afghan security forces.
Taliban fighters stormed several security checkpoints in Dih Yak and Jaghatu district of the Ghazni province late on Monday setting off a battle with the security forces that continued through Tuesday.
Seven police officers were killed in Dih Yak, including the district police chief Faizullah Toofan and reserve commander Haji Baraket. Seven others policemen were killed in Jaghatu district.
Taliban spokesman Zabihullah Mujahid claimed responsibility for the attacks in a statement to the media. He claimed the Jaghatu district headquarters was captured as well as several police checkpoints in Dih Yak.
The Taliban also issued a statement warning residents of the capital, Kabul, to avoid military and intelligence centres as they planned to target those as part of their spring offensive.
Since announcing their offensive in April, Taliban fighters have stepped up attacks across the country against Afghan security forces and government officials.
In a recent statement, the Taliban offered amnesty to Afghan police and military in the country if they left “enemy ranks”.