Irabor said the attackers were arrested during joint operations involving the armed forces, the Department of Security Services and police, privately owned Channels TV reported earlier.
It was not immediately clear how many suspects were taken into custody or where and when the arrests were made.
"It was my intention to present them to the public, but because of the investigation still going on, I had to change my mind," Irabor said in a statement.
"I will like to say that in due course, the world will see them and others who are behind other daring attacks in the country."
Nigerian authorities have said they suspect insurgent group Islamic State West Africa Province (ISWAP) carried out the massacre of members of a congregation inside the St Francis Catholic Church in the southwestern state of Ondo on June 5.
(Reporting by MacDonald DzirutweEditing by Mark Heinrich and Bernadette Baum)
