Gates said he regretted ties had been strained with key "war on terror" ally Pakistan over the incident, which Islamabad has slammed as an "unprovoked and cowardly" attack.

"We agree we need to investigate this incident. We've invited the Afghans and the Pakistanis to be a part of the investigation," Gates told reporters at a NATO meeting in Brussels.

"Pakistan is an incredibly important partner for us in this war on terror. Personally, I regret we've had something that has created a problem," he said.

"We've had an incident that has created a problem between us and the government of Pakistan."

The White House said it was still looking into reports that the coalition had killed Pakistani soldiers at a checkpost in the volatile Mohmand tribal zone, but that it would be "very saddened" if they proved accurate.

Officials in Washington had earlier said they regretted the "reported loss of Pakistani life" but insisted their forces carried out a "legitimate strike" -- and had given Pakistan advance warning.

Top US military chief Admiral Michael Mullen insisted the operation, carried out early on Wednesday, was "very much by the book."

"If there was these deaths of Pakistani military, it is incredibly regrettable," said the chairman of the joint chiefs of staff.

The coalition backed those claims with video showing "precision" strikes on a group of seven rebels who sought refuge in Pakistan after attacking a coalition reconnaissance patrol in eastern Afghanistan.

The black and white video footage, taken by an unmanned drone, shows a first strike targeted at men hiding behind a rock who fire two rocket-propelled grenades at coalition troops off-screen.

The US-led soldiers were attacked while trying to move to a pick-up point for extraction by helicopter when they were attacked by the "anti-Afghan forces," said a commentary supplied with the video.

A huge explosion lights up the area and the militants then seek cover in a deep ravine nearby before three more bombs, one of which is not shown, land on the militants.

"It is clear there are no structures or (Pakistani) outposts in the impact area," the voice-over said, adding that all of the militants were killed.

But an AFP photographer who reached the scene late Wednesday saw a large crater near a mud-brick Pakistani paramilitary outpost, which was badly damaged.

Local tribesmen were scraping pieces of human flesh from nearby trees, while shredded military uniforms and pools of blood littered the scene.

In the neighbouring tribal region of Bajaur, hundreds of armed tribesmen chanting "Death to America!" and "We are ready for jihad (holy war)!" staged a protest against the attack on Thursday.

The incident is the worst of its kind since President Pervez Musharraf sided with the United States in 2001 against the Taliban and Al-Qaeda, and comes amid growing international unease over Pakistan's recent negotiations with the Taliban.

Pakistani security officials and residents said the incident began when Afghan troops crossed the porous frontier and tried to occupy a strategic Pakistani post in a long-disputed area of the troubled tribal belt.

Residents said word spread in the conservative region and armed tribesmen along with Pakistani Taliban fighters arrived and attacked the Afghan soldiers, who retreated and returned later with coalition forces.

Pakistani Foreign Minister Shah Mehmood Qureshi has complained to NATO chief Jaap de Hoop Scheffer about the "unprovoked and senseless attack" on the sidelines of an Afghanistan donors' conference in Paris, a government statement said.

Using unusually harsh language, the Pakistani army had on Wednesday "condemned this completely unprovoked and cowardly act" and warned that it "hit at the very basis" of cooperation in the anti-terror fight.

Musharraf's support for Washington has angered many Pakistanis and drawn the wrath of militants.

His allies were voted out of office earlier this year, and the new government has sought to strike peace deals with militants in the restive tribal zones.

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