The Pakistani army launched a strong protest and reserved "the right to protect our citizens and soldiers against aggression," the military said in a statement. The statement said the clash in the Mohmand tribal region "had hit at the very basis of cooperation" between the two allies in the war on terror.
The U.S. military declined to comment.
The lawless and remote mountain region is difficult for reporters to access and there were conflicting reports over the sequence of events and how many died in the fighting. The region is believed to be used by pro-Taliban militants as a launch pad for attacks into Afghanistan.
That infiltration is a constant source of tension in the counterrorism alliance. Pakistan has deployed tens of thousands of troops to police its tribal regions, but Western and Afghan officials say that has not deterred militants. Afghanistan often accuses Pakistan of abetting the Taliban, whose hardline regime it supported until its ouster in 2001.
Pakistani officials said the fighting broke out Tuesday after Afghan troops tried to set up a mountaintop post in a contested part of the lawless frontier and Pakistani security forces told them to withdraw.
Local tribesman Damagh Khan Mohmand said the Afghan forces had moved into the area around Speena Sooka, or White Peak, on Monday evening and were supported by foreign troops. There was no confirmation of that from the U.S.-led coalition or NATO security force in Afghanistan.
Khan Mohmand said tribesmen traded fire with the Afghan and foreign forces, and said Pakistani security forces also opened fire - although the military disputed that.
The army said the coalition airstrike hit a post of the paramilitary Frontier Corps and was a "completely unprovoked and cowardly act."
Khan Mohmand said he saw drones and that two aircraft had bombed several locations.
Maulvi Umar, a spokesman for an umbrella group of Pakistani Taliban, said militants had resisted an incursion into Pakistan.
He said between 60 and 100 of its fighters attacked NATO and Afghan army troops who had set up bunkers and tents on Pakistani soil. He claimed up to 40 Afghan troops were killed, several captured and that a NATO helicopter was shot down. Eight Taliban troops also died in the fighting, he said.
None of his claims could be independently confirmed.
State-run Pakistan Television said 18 people died in the fighting, including 10 troops and eight civilians. It reported that Afghan and foreign forces had tried to set up a military post and were resisted by tribesmen. A NATO airstrike then struck a Pakistani military post, PTV said.
On Wednesday, two helicopters brought the bodies of 11 troops killed and another 13 soldiers wounded in the fighting to Peshawar, the main city in northwestern Pakistan, a military intelligence official said on condition of anonymity because he is not allowed to comment to the media. Witnesses said seven ambulances shifted the casualties to a military hospital in the city.
Officials in Afghanistan all declined comment.
NATO in Afghanistan referred inquiries to the U.S. military whose spokeswoman, Lt. Col. Rumi Nielson-Green, referred calls on reports of an airstrike to the U.S. Embassy in Pakistan. The embassy also declined comment. The Afghan Ministry of Defense said it had no information on the incident.
The U.S. has in the past used unmanned drones to attack suspected militants inside Pakistan.
Pakistan does not allow foreign troops to conduct military operations on its territory. It says aerial attacks launched from Afghanistan are a violation of its sovereignty.
