Six civilians were killed and 17 wounded on Sunday on the Pakistani side by Afghan fire, leading Pakistani troops to retaliate, the country's military said in a statement.
The Pakistani army accused the Taliban of using heavy weapons indiscriminately.
The death toll rose on Monday as two injured, including a 10-year-old boy, died in hospital in the south-western Pakistani city of Quetta, hospital official Wasim Baig said.
Relations between the Taliban and the Pakistani government have deteriorated in recent months, with mutual suspicion growing following rising violence between Tehreek-e-Taliban — the Pakistani branch of the movement — and Pakistani security forces in rugged northern border regions.
Tehreek-e-Taliban have long been accused of using Afghan territory to attack security forces in Pakistan. The Taliban also used the country as a sanctuary for raids into Afghanistan during the 20-year period of foreign occupation.
But there were hopes in Islamabad and Kabul that the Taliban victory in August 2021 — when international forces hurriedly left the country — would result in stronger co-operation.
A former Pakistani prime minister sparked international controversy when he welcomed the Taliban victory, saying the group had “broken the shackles of slavery”.
Clashes between Pakistani soldiers and the Taliban soon broke out, however, with fighting at the Chamal crossing killing three in November, leading Pakistan to halt the movement of trade there.
Both sides used to enjoy strong relations, with Pakistan being the Taliban’s main state backer during the 1990s, when the group last ruled much of Afghanistan.
Pakistan provided military support for the movement, playing a key role in keeping the Taliban’s basic air force flying during the Afghan civil war in the 1990s.
Pakistani Prime Minister Shehbaz Sharif said the killings “deserve the strongest condemnation”.
“The Afghan interim government should ensure that such incidents are not repeated,” he said in a statement.
Haji Zahid, a spokesman for Kandahar's governor, said the fighting began after Pakistan objected to Afghan forces building a new checkpoint.
“They didn't want us to build these posts on our side of the border,” he said and added that it led to a two-hour long gun battle.
Chaman is the second-largest commercial border point between the two countries after Torkham in Khyber Pakhtunkhwa. It is a vital source of customs revenue for the cash-strapped administration in Afghanistan.
Previous closures of the crossing involved disputes over issues ranging from Covid-19 to the validity of Afghan travel documents.
The crossing was closed for several hours on Sunday before reopening, officials on both sides said.
“Such unfortunate incidents are not in keeping with the brotherly ties between the two countries,” Pakistan's foreign office said. It added that Afghan authorities had been told that a recurrence must be avoided.