The Nato statement contradicted an Afghan defence ministry spokesman who had earlier accused a Pakistani officer of opening fire on US soldiers at the meeting, killing two and wounding two.
A spokesman for Pakistan's military appeared to agree with the Nato version of events.
"As the convoy [of US soldiers] was moving back, some miscreants fired. Three to four US soldiers and three to four Pakistani soldiers were injured," Major-General Waheed Arshad said.
Pakistani officials regularly use the term miscreants in reference to anti-government fighters, especially the Taliban and those linked to al-Qaeda.
In another account of the incident, a senior Pakistani security official said the Isaf soldiers were shot at by a man "disguising himself" as a Pakistani paramilitary soldier.
The governor of Afghanistan's Paktia province gave yet another version of events.
"When the results of the talks were announced and the delegation was getting back on helicopters, a Pakistan military militia officer opened fire at us," said Rahmatullah Rahmat, who said he was part of the Afghan delegation at the meeting.
He said two soldiers from the 12,000-strong US-led coalition that operates separately from Isaf in Afghanistan were killed, a claim contradicted by both foreign forces.
General Mohamad Zahir Azimi, Afghan defence ministry spokesman, said that "in the course of the meeting, one Pakistan officer opened fire and unfortunately two American officers were killed".
Arshad called the Afghan version of events "completely incorrect".
The relationship between Pakistan and Afghanistan has come under increasing strain in recent months over allegations that Taliban and al-Qaeda-linked fighters based on Pakistani soil are launching attacks in Afghanistan with the backing of Islamabad.