The strikes early Thursday killed at least 30 people, many of them children, after a Taliban assault left two American soldiers and three Afghan special forces soldiers dead in the Boz-e-Kandahari area near the provincial capital.
"The president of Afghanistan has sent a special delegation to Kunduz to investigate the incident. Any negligence by anyone will be punished," presidential spokesperson Haroon Chakhansuri told reporters.
US military spokesperson Charles Cleveland said an initial probe showed the attack "very likely resulted in civilian casualties".
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The carnage triggered impassioned protests in Kunduz city, with the victims' relatives parading mutilated bodies of dead children piled into open trucks through the streets.
"Look around me -- everyone is in deep pain," Sultan Mohammad said, carrying the body of a victim for the mass funeral ceremony on Friday.
"What was their crime? Why were they killed like this?"
He joined a growing chorus of people calling to bring the perpetrators to justice.
The carnage underscores worsening insecurity after the Taliban last month overran the city for the second time in a year, as NATO-backed Afghan forces struggle to rein in the insurgents.
US-backed Afghan special operations forces were conducting an operation against the Taliban on the outskirts of Kunduz city when they came under insurgent fire, prompting calls for air support.
"I deeply regret the loss of innocent lives, regardless of the circumstances. The loss of innocent life is a tragedy and our thoughts are with the families," said John Nicholson, the top US and NATO commander in Afghanistan.
30 Afghan civilians killed in Kunduz NATO airstrike
"We will work with our Afghan partners to investigate and determine the facts."
The strikes also killed some top Taliban commanders, defence ministry spokesperson Daulat Waziri said.
"Some civilians killed were members of their families," he added.
Civilian casualties caused by NATO forces have been one of the most contentious issues in the 15-year campaign against the insurgents, prompting strong public and government criticism.
Errant air strikes contributed to a 42 percent jump this year in casualties caused by pro-government forces compared to last year, according to the UN.
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