Taliban authorities on Saturday summoned Pakistan's ambassador in Kabul to protest against military strikes inside Afghanistan by Pakistani forces, the Afghan foreign ministry said.

A local Taliban official and residents said 36 people were killed in air strikes on Friday by Pakistani aircraft entering Afghan airspace. Pakistan denied it carried out the strikes.

Islamabad claims militants carry out attacks inside Pakistan by crossing its lawless western border with Afghanistan. Taliban authorities say they have controlled the attacks since taking over the country in August last year.

A statement from Afghanistan's Ministry of Foreign Affairs said Pakistan's Ambassador in Kabul had been summoned over the recent attacks in Khost and Kunar provinces and given a diplomatic demarche to deliver to Islamabad.

"Military violations including those in Khost and Kunar must be prevented as such acts deteriorate relations ... allowing antagonists to misuse the situation leading to undesired consequences," the statement quoted acting Afghan Foreign Minister Amir Khan Muttaqi as saying.

The statement did not elaborate on the nature of the strikes, but a local Taliban leader in Khost, Mawlawi Mohammad Raes Helal, said two districts were bombed by Pakistani helicopters and that 36 people had been killed.

The claim was echoed by some residents, but the Pakistan embassy spokesman denied there had been air strikes and told Reuters the ambassador and Taliban authorities discussed a resolution of border issues.

There was no official confirmation of the death toll.

Pakistan has enjoyed good relations with the Taliban for years even though Islamabad was officially an ally of the United States during its 20-year occupation of Afghanistan.

Since the Taliban took over Afghanistan, there have been numerous standoffs along the 2,600 km (1,615 mile) border with Pakistan - drawn by British colonial rulers and disputed by Kabul.

Increasingly frustrated by continuing militant attacks, Pakistan's military has stepped up operations along the Afghan border in recent months.