According to government officials, scores of armed tribesmen from Bangash and other tribes have started assembling to support the security personnel.
According to the ISPR, Afghan Border Police opened fire on FC Balochistan personnel who were deployed in the area to provide security to the Population Census team.
Initially, Afghan National Police interim chief Colonel Abdul Hanan told Anadolu Agency that two Pakistani troops were arrested during the clash.
Afghanistan has refused to recognise the Durand Line - a 2,400-kilometre frontier drawn by the British in 1896 - as it splits the Pashtun ethnic group between the nations.
In a separate incident on Sunday in Pakistan's North Waziristan district, which also borders Afghanistan, a security forces vehicle was struck by an improvised explosive device 15km from district capital Miranshah, a military official said.
The bodies of the two Pakistanis were found on the Afghan side of the border near Pakistan's tribal belt, Zadran told AFP.
Clashes are still underway, he said.
Afghan officials often give conflicting casualty figures.
The Inter-Services Public Relations (ISPR), the media wing of Pakistan army, said that the personnel of Frontier Constabulary, a paramilitary force, came under attack from the Afghanistan side when they were carrying out a routine surveillance at the Pak-Afghan border in Kurram Agency, the country's northwest tribal region.
Khost provincial governor spokesman Talib Mangal confirmed the incident, but said two Afghan civilians and four Pakistani troops were killed.
Kabul has long-accused Islamabad of providing safe havens for the Afghan Taliban, which has been waging an insurgency in Afghanistan for more than 16 years.
The army is in the process of fencing the porous Pak-Afghan border in a bid to stem the free-flow of militants.