Zakir Hussain Sultani, the deputy provincial governor in Wardak, says the assault came on Wednesday night and that the Taliban captured five of the checkpoints attacked in Jalrez district.
Sultani says intense fighting is still underway in the area on Thursday. He says a roadside mine has struck two Afghan army tanks.
Wardak is one of the gates to Kabul and the Taliban control most of the rural parts of the province.
A statement from the Taliban, who launched their annual spring offensive in April, said they were behind the attack in Jalrez district.