Trucks and fuel tankers for foreign forces in Afghanistan were stopped at the Torkham border post in the Khyber tribal region near Peshawar, hours after the raid.
“Yes, the NATO supplies have been stopped. It has been done locally,” a senior security official said.
Aircraft from the NATO-led International Security Assistance Force (ISAF) initially crossed the border in the Kurram region briefly while targeting suspected insurgents who were firing on a coalition base from a position inside Afghanistan, the statement said.
They were then fired on by people in Pakistan, and crossed the border again to target that group.
“Operating in self-defence, the ISAF aircraft entered into Pakistani airspace killing several armed individuals,” the statement said.
The statement did not say if ISAF thought those killed were border guards, and when asked for clarification, an ISAF spokeswoman said both sides were still investigating the incident.
“This is the third incident of its kind during the past week,” the Pakistani military said in a statement. Three soldiers were wounded, it said.
Pakistan is a crucial ally for the United States in its efforts to stabilise Afghanistan, but analysts say border incursions and disruptions in NATO supplies underline growing tensions in the relationship.
The United States has already stepped up missile strikes by its pilotless drone aircraft on militant targets inside Pakistan.
The bulk of non-lethal military supplies for NATO troops in Afghanistan moves through Pakistan.
The border row occurred as CIA chief Leon Panetta began a previously scheduled visit to Pakistan for talks with top military and political figures.
Panetta met President Asif Ali Zardari, Prime Minister Yusuf Raza Gilani, army chief General Ashfaq Kayani and the head of the powerful Inter-Services Intelligence (ISI) agency, Lieutenant-General Ahmed Shuja Pasha.
Gilani expressed “profound concern” over increasing drone strikes and violations of Pakistan’s airspace by NATO forces, he said in a statement.