The countries have traded fire along the border since Saturday, when dozens were killed across multiple border regions.
Afghanistan claimed to have killed 58 Pakistani soldiers in overnight operations in retaliation for what it called repeated violations of Afghan territory and airspace. Pakistan's army said 23 troops were killed.
The fighting on Wednesday erupted before dawn, according to officials on both sides. Pakistan TV, the main state-owned television station, reported later in the day that Afghanistan was seeking a ceasefire on the border near the village of Chaman where the fighting was concentrated.
Pakistani security officials and state-run media accused Afghan troops of "unprovoked fire" that was repulsed in Kurram, a district of northwestern Khyber Pakhtunkhwa province.
Security officials and television reports said Pakistan's military overnight killed 30 Afghan Taliban fighters near Kurram in Afghanistan's Khost province, destroyed a large training facility in Afghanistan used by the Pakistani Taliban.
On Tuesday, Pakistan's military said the Afghan Taliban worked with the Pakistani Taliban in an attempted assault on Pakistani border posts in the Kurram district but the attacks were repulsed, causing "heavy losses" to Afghan positions.
The clashes on the long and porous border stopped temporarily Sunday following appeals from Saudi Arabia and Qatar, but border crossings remain closed.
The renewed fighting underscores the simmering tension between the neighbours. The Taliban government on Friday accused Pakistan of carrying out air strikes in Kabul and in an eastern Afghanistan market.
This is the second time this week that the two sides have traded fire along their long border.
Over the weekend, Kabul said that it targeted several Pakistani military posts and killed 58 Pakistani soldiers in retaliation for what it called repeated violations of Afghan territory and airspace.
Pakistan's military reported lower figures, saying it lost 23 soldiers and killed more than 200 "Taliban and affiliated terrorists" in retaliatory fire along the frontier.
Tensions have remained high since last week, when the Taliban government accused Pakistan of carrying out air strikes in Kabul and in an eastern market. Pakistan has not acknowledged those allegations.
But Pakistan has previously launched strikes inside Afghanistan, saying it targets hideouts of Tehreek-e-Taliban Pakistan, or TTP, which is separate from but allied to the Afghan Taliban.
Pakistan accuses Kabul of harbouring the group, which has carried out numerous deadly attacks inside Pakistan. Kabul denies the charge, saying it does not allow its territory to be used against other countries.
