'Catastrophic event'
Aid agencies assisting the hundreds of thousands of people in northeast Nigeria in dire need of food, shelter, clean water and healthcare expressed shock and dismay at the bombing.
The UN High Commissioner for Refugees, Filippo Grandi, described it as "a truly catastrophic event", calling for a full investigation to prevent any repeat.
Jean-Clement Cabrol, director of operations for the medical charity MSF, which earlier gave a death toll of 52, said the attack was "shocking and unacceptable".
The secretary-general of the Norwegian Refugee Council, Jan Egeland, said: "It cannot become the new normal that 'accidental' attacks on camps sheltering the innocent are allowed to happen again and again in conflict zones."
Human Rights Watch's senior Nigeria researcher Mausi Segun said the government in Abuja should compensate victims and their families.
"Even if there is no evidence of a wilful attack on the camp, which would be a war crime, the camp was bombed indiscriminately, violating international humanitarian law.
"Victims should not be denied redress merely because the government decided the bombing was accidental."
Accidental bombings have occurred before in the conflict and senior military commanders called the latest "a mistake", saying humanitarian workers were not targeted directly.
Major General Lucky Irabor, who heads the counter-insurgency operation, said the air force jet had been told to target insurgents in the flashpoint Kala-Balge area but hit Rann instead.
A delegation headed by President Muhammadu Buhari's chief of staff Abba Kyari and including armed forces chiefs visited Maiduguri on Wednesday and was also scheduled to visit Rann.
Kyari called the bombing "very unfortunate" and noted "incidents of friendly fire are as old as history of mankind" but said that was no excuse and he was happy there was no cover up.