Nigeria's military has said it killed 50 members of the armed group Boko Haram as they tried to cross Cameroon's border.
Fifteen soldiers and five civilians were also killed in Monday's battle, it said.
Boko Haram wants to carve out an Islamic state in a country split roughly equally between Christians and Muslims.
Since starting its uprising in 2009, the sect has turned itself from a clerical movement opposed to Western culture into an militia with links to al-Qaeda's West African wing.
Nigerian forces stepped up their military offensive in the northeast after Boko Haram fighters, armed with grenade launchers and anti-aircraft weapons, attacked their barracks in the town of Bama on Friday.
Several soldiers' wives and children were abducted during the attack.
Nigeria's army also engages in the practice of seizing relatives as a way to get suspects to give themselves up.
The military rarely admits casualties among its own troops or civilians.