The Taliban forces said they attacked Pakistani army at the border between Afghanistan and Pakistan in retaliation for deadly strikes earlier this week, capturing several army outposts.
The Taliban military forces have attacked Pakistan at the border between the two countries on Thursday, Kabul has said.
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The "large-scale offensive operations" were in response to deadly air strikes on Afghanistan earlier this week, military and government officials said.
A Taliban military spokesperson said that "heavy attacks on Pakistani outposts" were under way, with "no casualties on Afghan side". A separate Taliban government spokesperson said that 15 Pakistani army outposts were captured in the operations.
The Pakistani government did not provide an immediate reaction to the Afghan claim.
The military operation follows Pakistani strikes on Nangarhar and Paktika provinces overnight into Sunday, which the UN mission in Afghanistan said killed at least 13 people.
The Taliban government said at least 18 people were killed and denied Pakistan's announcement that the military operation left more than 80 militants dead.
Both sides also reported cross-border fire on Tuesday, but without casualties.
Relations between the neighbouring countries have deteriorated in recent months, with land border crossings largely shut since deadly fighting in October that killed more than 70 people on both sides.
Islamabad accuses Kabul of failing to act against militant groups that carry out attacks in Pakistan, which the Taliban government denies.
Pakistan's military launched its latest round of air strikes on Afghanistan following a series of deadly suicide blasts.