The grainy, monochrome images - taken by an unmanned drone - show a small group of men firing small arms and rocket-propelled grenades from a ridge at coalition troops who were off camera in the valley below.
The voiceover on the footage said that the ridge was in the Afghan province of Kunar, about 182m (200 yards) from the Pakistan border.
"It is clear there are no structures or (Pakistani) outposts in the impact area," the voiceover said.
It said that coalition forces were on a reconnaissance mission in the area at the time of the attack and were waiting for a helicopter to pluck them to safety.
The video showed "anti-Afghan militants" moving to positions it said were inside Pakistan and the impact of a bomb which the voiceover said killed two of them.
The survivors then fled into a cave, the video voiceover said, where three more bombs were dropped nearly three hours after the clash started. The voiceover said all the militants were killed and that about 12 bombs were dropped in all.
Earlier, the US state department described the deaths of Pakistani soldiers in the air attack as regrettable, and said there was a need for better communication.
A hillside appeared to have been stripped bare by fighting
The incident took place on Tuesday night at a border post in the mountainous Gora Prai region of Mohmand, one of Pakistan's tribal areas, across the border from Kunar province.
The Pakistani government summoned the American ambassador to protest in person about the disputed attack.
It comes at a time of tension between Pakistan and the US over how to deal with militants in border areas, the BBC's Kim Ghattas reports from Washington.
"Every indication we have at this point is that this was indeed a legitimate strike in defence of our forces after they came under attack," coalition spokesman Geoff Morrell told reporters.
Expressing regret, the US state department said the incident was a reminder that "better cross-border communications between forces is vital".
The 11 Pakistani soldiers were buried on Wednesday in the north-western city of Peshawar.
A Pakistani army statement said the incident had "hit at the very basis of co-operation" with the US.
Prime Minister Gilani condemned the deaths in parliament saying that Pakistan's sovereignty was at stake.
Funerals have been held for the 11 soldiers who died
A spokesman for a pro-Taleban militant group in Pakistan said it had launched an attack on US and Afghan troops trying to set up a border control post.
In Peshawar, a relative of the one of those wounded in the fighting said that US troops had opened fire on both tribespeople and Pakistani soldiers.
"Then suddenly bomber aircraft came and started bombing," Seed Aman told The Associated Press.
There is increasing anger in Pakistan at US strikes on its territory which have killed more than 50 people this year, says the BBC's Barbara Plett in Islamabad.
Taleban fighters have a strong presence in the border areas of the tribal districts and local administrators have little power there.
There is rising frustration among Nato and Afghan troops at Pakistani efforts to negotiate peace deals with pro-Taleban militants on its side of the border.
Afghan and US-led forces accuse Islamabad of not doing enough to deny Taleban militants a hiding-place in Pakistan's tribal areas and to stop them from infiltrating the border.
Pakistan denies the accusations, saying it has lost about 1,000 soldiers fighting militants in the tribal border areas.
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