President Muhammadu Buhari has visited Kuje prison in the federal capital territory (FCT).
Gunmen had attacked the prison with explosives on Tuesday night.
A resident had told TheCable that gunshots were heard for over 30 minutes, causing panic among residents.
The ministry of interior said about 600 inmates escaped from the correctional facility.
The president, who is presently touring the scene of the attack, is expected to depart for Dakar, Senegal, later today.
Buhari was accompanied to the prison by Usman Baba, the inspector-general of police (IGP), and Haliru Nababa, comptroller-general of the Nigerian Correctional Service (NCoS).
Bashir Magashi, minister of defence, had earlier said the attackers are Boko Haram insurgents.
He said 64 members of the terrorist group, who were inmates in the facility, cannot be found.
“They came in their numbers and released some of the inmates,” he said.
“We are trying to see what we can do to see that all escapees within the prison accommodation are brought back to the prison yard.
“About 994 inmates, we have about 600 already inside now. Many people are being recaptured. The people who came to do this from the records belong to a particular group, from all indicators they are Boko haram.
“Presently we could not locate any of them. Currently, they are about 64 of them as inmates and we could not locate them.”
