PARACHINAR, Pakistan — Pakistan blocked a vital supply route for U.S. and NATO troops in Afghanistan on Thursday in apparent retaliation for an alleged cross-border helicopter strike by the coalition that killed three Pakistani frontier troops.

The blockade appeared to be a major escalation in tensions between Pakistan and the United States. A permanent stoppage of supply trucks would place massive strains on NATO and hurt the Afghan war effort.

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"We will have to see whether we are allies or enemies," Pakistani Interior Minister Rehman Malik said of the border incident, without mentioning the blockade.

NATO said in a statement Thursday that aircraft from the NATO-led International Security Assistance Force (ISAF) crossed the border into Pakistan Thursday morning and killed "several armed individuals."

The aircraft initially crossed the border 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.

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.

The coalition has, on at least one occasion in the past, acknowledged mistakenly killing Pakistani security forces stationed close to the border.

Over the weekend, NATO helicopters fired on targets in Pakistan at least two times , killing several suspected insurgents they had pursued over the border from Afghanistan. Pakistan's government protested the attacks, which came in a month during which there have been an unprecedented number of U.S. drone missile strikes in the northwest, inflaming already pervasive anti-American sentiment among Pakistanis.

The surge in attacks and apparent increased willingness by NATO to strike targets on the border or just inside Pakistan, could be a sign the coalition is losing patience with Pakistan, which has long been accused of harboring militants in its lawless tribal regions.

Pakistani security officials said Thursday's deadly airstrike took place on a checkpoint in the Upper Kurram region.

The dead men were from a paramilitary force tasked with safeguarding the border, the security officials said. Their bodies were taken to Parachinar, the region's largest town, one official said. Three troops also were wounded.

"The helicopters shelled the area for about 25 minutes," a Pakistani security official told Reuters.

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The security officials spoke on condition of anonymity because of the sensitivity of the situation and because in some cases they were not authorized to release the information to the media.

The border between Pakistan and Afghanistan is unmarked. Border troops wear uniforms that resemble the traditional Pakistani dress of a long shirt and baggy trousers, which could make it hard to distinguish them from ordinary citizens or insurgents.

U.S. officials have complained in the past that Pakistani security forces do little to stop the movement of militants seeking to cross over into Afghanistan and attack foreign troops there.

Lt. Col. John Dorrian, a spokesman for intelligence and special operations at NATO headquarters in Kabul, said coalition forces observed early Thursday what they believed were insurgents firing mortars at a coalition base in Dand Wa Patan district of Paktia, which is next to Upper Kurram.

"A coalition air weapons team called for fire support and engaged the insurgents," he said. "The air weapons team reported that it did not cross into Pakistani air space and believed the insurgents were located on the Afghan side of the border."

Dorrian said Pakistani military officials had informed the NATO military coalition that members of their border forces had been struck by coalition aircraft. He said the coalition was reviewing the reports to see if the operation in Paktia was related to those reports.

Hours after the incident, Pakistani authorities were ordered to stop NATO supply trucks from crossing into Afghanistan at the Torkham border post, a major entryway for NATO materials at the edge of the Khyber tribal region, two government officials said.

By midmorning, there was a line of around 100 NATO vehicles at the checkpoint, the officials said.

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The other main route into Afghanistan in southeastern Pakistan had received no orders to stop NATO trucks from crossing, which they were doing as normal, said Syed Mohammed Agha, a spokesman for the Pashin Scouts border guards.

Some 80 percent of non-lethal supplies for foreign forces fighting in landlocked Afghanistan are transported over Pakistani soil after being unloaded at docks in Karachi, a port city in the south. While NATO and the United States have alternative supply routes, the Pakistani ones are the cheapest and most convenient.

Though many analysts believe that the strikes by unmanned U.S. drones are carried out with the tacit approval of Pakistan, any border incursions by foreign troops is a highly explosive issue in Pakistan.

In June 2008, a U.S. airstrike killed 11 Pakistani troops and frayed the two nations' ties. Pakistan said the soldiers died when U.S. aircraft bombed their border post in the Mohmand tribal region. U.S. officials said their coalition's aircraft dropped bombs during a clash with militants. They expressed regret over the deaths, but said their attack was justified.

Pakistan and the U.S. have a complicated, but vital, relationship, with distrust on both sides.

Polls show many Pakistanis regard the United States as an enemy, and conspiracy theories abound of U.S. troops wanting to attack Pakistan and take over its nuclear weapons. The Pakistani government has to balance its support for the U.S. war in Afghanistan — and its need for billions in American aid — with maintaining the support from its own population.