A senior Afghan defence ministry official said the air attack happened during a meeting of militants, and killed at least 35 Taliban and wounded many more.
Abdullah Qarloq, a senator from the district, said the Afghan military struck the Akhundzada Gojor madrassa, or religious school, during a graduation ceremony.
"Twenty Taliban, including the commander of their Red Unit in the district, and also a key member of the Quetta Shura were killed", Mohammad Radmanish said.
Radmanish claimed Taliban fighters fired back at army helicopters with anti-aircraft guns during the aerial operation and later they intentionally sprayed civilians in the area with bullets.
A spokesman for the Taliban, Zabihullah Mujahid, said that the death toll was far higher than the official figure and that no insurgents had been present at the gathering, which was strictly religious in nature.
"There were children as young as 11 or 12 years old in the ceremony who were to be presented with awards and gifts for the completion of their religious courses", Mohammed Abdul Haq, who witnessed the attack, told the worldwide media.
" Mothers are crying outside the hospitals for their dead children and everyone is crying with them", this individual included. The farmer was unable to say how many had been killed or hurt, but added that one of the wounded was his nephew, age 10.
" I was working in my farm when I heard helicopters and jets bombing the madrassa (spiritual academic institution) where the Taliban were gathered alongside new Qaris (the ones who memories the 30 chapters of the Quran) to recognise them with awards", Haji Ghulam shared. The city has been considered relatively secure over the past year or two but the Taliban control much of the surrounding area.
Nonetheless, witnesses said that children and other civilians were among the victims.
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"It was a disaster. Blood everywhere", he said, adding that the "many" people were killed.
Photos flowing on the social media sites revealed a variety of young children have been eliminated, followed by the expression: "I am not a terrorist". Al Jazeera could not independently verify the images. The Taliban, for its part, denied the presence of its fighters in the area, saying in a statement that more than 100 clerics and other civilians were killed at an Islamic religious school.
The group denied its fighters were at the school.
"UNAMA actively looking in to disturbing reports of serious harm to civilians yesterday from airstrike at #DashtiArchi, #Kunduz".
However, Patricia Gossman, a senior researcher for Human Rights Watch in Afghanistan, fears that many of those killed might have been civilians. "All parties reminded of obligations to protect civilians from the impact of armed conflict", the tweet said.
According to the residents and some provincial council members, the airstrike was carried out by the Afghan Air Force (AAF) on a madrassa.
Earlier he had said 20 Taliban were killed.
Monday's airstrike underscores a potential pitfall in the latest US strategy in the 16-year war in Afghanistan, which calls for significant investment in the Afghan air force.