At least three people have been killed in northeastern Afghanistan following Pakistani air raids, Afghan officials said.

Kunar provincial spokesperson Farid Dehqan said the attack struck the Nurgal district at around 4am local time on Monday, killing three people and injuring four.

Taliban deputy spokesperson Hamdullah Fitrat said at least one house in Kunar, a mountainous province in northeastern Afghanistan, was hit in the strikes. He said three members of the same family were killed and four others injured.

"In the Barmal district of Paktika province, two locations were bombarded, destroying one shop and one unoccupied house, with no casualties reported," Fitrat said.

Pakistan's information ministry said 28 "terrorists" were killed in air strikes on three targets inside Afghanistan. There was no immediate further comment from Pakistan on the reported attacks.

The strikes threaten to reignite tensions between the two neighbours after nearly three months of relative calm. Relations between the former allies have been strained since February, when the two sides fought their worst clashes in years.

The dispute centres on violence inside Pakistan. Islamabad accuses Kabul of harbouring armed groups that carry out cross-border attacks from Afghan territory. Afghanistan's Taliban government denies the charges and says the violence is Pakistan's internal problem.

The air raids came days after a Pakistan Taliban faction claimed responsibility for a bombing at a mosque inside a police facility in Kohat, in northwestern Pakistan. The blast and a subsequent gun battle killed at least 21 people, mostly police officers, Pakistani officials said.

Pakistan's Ministry of Information warned on Saturday that the country could strike fighters inside Afghanistan in response to attacks on Pakistani soil. The ministry blamed the Kohat attack on fighters it said were based in Afghanistan.