KABUL, Afghanistan — Pakistan brought a critical NATO supply route for U.S.-led forces in Afghanistan to an abrupt halt on Thursday after NATO aircraft crossed into Pakistan in a confused attack that killed three Pakistani paramilitary troops.

Pakistan shuttered its main border crossing with Afghanistan hours after NATO helicopters apparently hit a Frontier Corps border post during a border battle with insurgents.

Hundreds of trucks bound for the Torkham crossing were halted as NATO said it was investigating the incident.

Without directly claiming responsibility for the incident, the U.S.-led military issued a statement conveying "sincere condolences to the Pakistani military and the families of those who were killed or injured."

In a statement, NATO said that its helicopters crossed into Pakistani airspace while battling insurgents firing mortars at U.S-led troops.

"After the initial strike, the aircraft received what the crews assessed as effective small arms fire from individuals just across the border in Pakistan," NATO said. "Operating in self defense, the ISAF aircraft entered into Pakistani airspace killing several armed individuals."

While NATO officials launched an investigation, the border closure disrupted the critical supply route and raised tensions between the United States and Pakistan.