The military has said troops were carrying out aerial patrols on Sunday when they observed a group of people in northwest Kaduna State and "misinterpreted their pattern of activities" to be similar to that of bandit militias.
A drone mistakenly struck the village of Tudun Biri as residents celebrated a Muslim festival.
Official sources said at least 85 people were killed and 66 others injured.
Nigeria's armed forces often rely on air strikes in their battle against bandit militias in the northwest and northeast of the country, where jihadists have been fighting for more than a decade.
Visiting a Kaduna hospital where the wounded from the attack were receiving treatment, Vice President Kashim Shettima told local television that the government would investigate and punish anyone found culpable.
The victims will also be cared for, he added.
President Bola Ahmed Tinubu has ordered an inquiry into the incident.
Muslim organisation Fityanul Islam of Nigeria said in a statement on Thursday that "all arguments advanced by the army about 'mistaken identity' are grossly inadequate, unfair and seemingly insensitive".
"Military authorities must therefore come clean with more transparent information" on the attack, it urged.
- UN call for compensation -
Amnesty International gave its own death toll of more than 120 civilians.
It said in a statement that Tinubu's administration must "promptly" set up an independent inquiry and "where these investigations indicate criminal responsibility, ensure that those suspected to be responsible are brought to justice in fair trials".
The UN human rights office on Wednesday deplored the attack, noting it was the latest of at least four air strikes that have resulted in significant civilian deaths since 2017.
The UN called on Nigeria to review its rules of engagement and operating procedures to ensure such incidents do not happen again and to compensate the victims and their families.
Protesters took to the streets in Zaria near the site of the attack on Wednesday as well as in front of the National Assembly in the capital Abuja to demand sanctions against the army.
Chief of Defence Staff General Christopher Gwabin Musa said on national television the same day that "mistakes do happen", before calling for an increase in the army's budget.
Tinubu has made tackling insecurity a priority since coming to office in May, as he seeks to encourage foreign investment in Africa's most populous country.
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