Commissioner Mohamed Abubakar Jinjiri told the BBC Hausa service that five people had been killed in the attacks. He said that among the arrested was a suspected Boko Haram financier, who had bomb-making equipment in his house.
So far 92 people had been arrested since the attacks on Wednesday in the city of Maiduguri.
The attackers are suspected of being members of the Boko Haram sect.
Clashes between the group and the police have left hundreds dead since last year.
Boko Haram claimed responsibility for the Christmas Eve bombings in the central city of Jos that killed some 80 people.
An army spokesman, Lt Abubakar Abdullahi, told the AFP news agency that eight people were killed in five separate attacks.
He said the Islamists burnt out a police patrol van in the attack in which the three officers were killed.
AFP quoted a Borno state police spokesman, Lawal Abdullahi, as saying that suspected Boko Haram gunmen had also killed a policeman and a retired officer and injured three civilians on Tuesday.
Hundreds of people suspected of being Boko Haram members escaped from prison in September after gunmen attacked the jail where they were being held.
The group, which is known locally as the Taliban, wants Islamic law imposed across Nigeria.
Last year hundreds of people, mostly members of the sect, died after Boko Haram members attacked a police station in Maiduguri and clashes spread to neighbouring areas.