The Taliban in return issued a warning to Islamabad over alleged attacks by the Pakistani military that killed at least six Afghan civilians.
Tension between the countries has risen since the Taliban seized power last year, with Islamabad claiming militant groups are carrying out regular attacks from Afghan soil.
The Taliban deny harbouring Pakistani militants but are also infuriated by a fence Islamabad is erecting along the 2,700-kilometre border that separates the countries.
Tension erupted after five children and a woman were killed in the eastern Afghan province Kunar on Saturday in alleged rocket attacks that Afghan officials blamed on the Pakistani military.
A similar pre-dawn assault was carried out in Afghanistan’s Khost province near the border, a local Taliban leader said.
Mawlawi Mohammad Raes Helal told Reuters two districts were bombed by Pakistani helicopters and that 36 people had been killed.
While the Pakistani military has not confirmed whether it carried out the attacks, Islamabad insisted it was facing continuous “terrorist” attacks from across the border.
“Pakistan, once again, strongly condemns terrorists operating with impunity from Afghan soil to carry out activities in Pakistan,” the Foreign Ministry said in a statement on Sunday.
“Pakistan requests the sovereign Government of Afghanistan to secure Pak-Afghan Border region and take stern actions against the individuals involved in terrorist activities in Pakistan.”
Seven Pakistani soldiers were killed in North Waziristan district on Thursday by “terrorists operating from Afghanistan”, the ministry said.
Areas along the border have long been a stronghold for militant groups such as Tehreek-e-Taliban Pakistan, which operates across the porous frontier with Afghanistan.
“Unfortunately, elements of banned terrorist groups in the border region, including TTP, have continued to attack Pakistan’s border security posts, resulting in the martyrdom of several Pakistani troops,” the ministry said.
The Afghan Taliban and the TTP are separate groups in both countries, but share a common ideology and draw in people who live on either side of the border.
Thousands of people usually cross the border daily, including traders, Afghans seeking medical treatment in Pakistan, and people visiting relatives.
Afghanistan’s Taliban government gave a warning to Pakistan after the rocket attack.
“This is a cruelty and it is paving the way for enmity between Afghanistan and Pakistan,” Taliban government spokesman Zabihullah Mujahid said late on Saturday.
“The Pakistani side should know that if a war starts it will not be in the interest of any side."
Afghan Foreign Minister Amir Khan Muttaqi summoned Pakistan’s ambassador on Saturday.
“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,” a statement quoted Mr Muttaqi as saying.
The UN Assistance Mission in Afghanistan (Unama) said it was “deeply concerned” by civilian deaths caused by air strikes and the mission was verifying the extent of losses.
Tolo News, an Afghan private TV channel, showed footage of houses destroyed in the attack in Khost.
“All the targeted people were innocent civilians who had nothing to do with the Taliban or the government,” Rasool Jan, a resident of Khost, told the channel.
“We don’t know who is our enemy and why we were targeted.”
Hundreds of Khost residents poured into the streets chanting anti-Pakistan slogans later on Saturday, photographs obtained by AFP showed.