The group made the claim in a new video, in which its leader, Abubakar Shekau, was again missing.
In the eight-minute video, an unidentified young man speaking in Hausa with Kanuri accent, said Boko Haram members remain on the ground.
“We are still present everywhere we had been before,” he said.
The video shows the group launching attacks on the security checkpoint, seizing weapons, and cutting the throat of unidentified middle aged man dressed in a police uniform.
The absence of Mr. Shekau in the new video raises question again about whether he is still alive or dead.
He was absent in an earlier video from the group in July.
The group also called on Muslims to reject the Muhammadu Buhari government.