The Pakistani soldiers were killed on Tuesday at a border post in Gora Prai, in the volatile Mohmand province, a tribal region in Pakistan opposite Afghanistan's Kunar province.
Geoff Morrell, the US department of defence spokesperson, said at a news conference on Wednesday: "Every indication we have is that this was a legitimate strike against forces that had attacked members of the coalition."
The video footage, taken by an unmanned drone aircraft, shows what are described by a man speaking off-camera as "precision-guided munitions" striking a group of seven men.
US military officials said fighters opposed to the Afghan government had taken refuge across the border in Pakistan after attacking a US-led patrol in Afghanistan's eastern Kunar province with small arms and grenade launchers.
The footage shows a first strike targeted at men hiding behind a rock, and three subsequent attacks on men seeking cover in a ravine.
"It is clear there are no structures or [Pakistani] outposts in the impact area," the commentator on the video said.
Major-General Athar Abbas, a Pakistan military spokesman, told Al Jazeera the attack was "unprovoked and cowardly … we blame the coalition forces … it has hit hard at the basis of our co-operation".
"We have co-ordination, we have intelligence-sharing.
"If there was some doubt about any post they should have informed us before taking up any strike," he said.
Kamal Hyder, Al Jazeera's correspondent in Islamabad, said: "The clashes are said to have involved an area ... called the White Peak, which is a contested area between Afghans and the Pakistanis.
"We were told that 80 Afghan and US forces occupied this area. They wanted to set up a forward post, we were told, but they were met with resistance. After that, the drones and bombers went into action.
"There big questions now as to why the Americans want to set up a forward base at this peak."
The US has given Pakistan $10bn in military aid since 2001, but US officials complain that Pakistan has done little to crack down on al-Qaeda or the Taliban in the rugged and largely lawless region along the Afghan border.
"The is a tendency for people in Pakistan to criticise the alliance with the Americans," Hyder said.
"Now they will have more ammunition to tell their government to back out of that alliance."
The senior US military spokesperson in Afghanistan, Lieutenant-Colonel Rumi Nielson-Green, told Al Jazeera that US-led forces had hit the "right target".
"The people involved in this incident … were firing on coalition forces and they were well inside of Afghanistan when they began the firing," she said.
Yousaf Raza Gilani, Pakistan's prime minister, said it was an affront to national sovereignty.
"We will take a stand for sovereignty, integrity and self-respect and we will not allow our soil [to be attacked]," he told parliament on Wednesday.
An Afghan village, just across the border from Pakistan, is also counting the cost of an air raid by the US-led forces in Afghanistan, Al Jazeera's Zeina Awad said.
The governor of Paktika Province says at least 40 people, including nine civilians, were killed when Ibrahim Kareez village was bombed on Tuesday.
A coalition statement said that the attack targeted "two militant leaders" and that just four civilians had died.
Source: Al Jazeera and agencies