Brig. Gen. Chris Olukolade, a military spokesman, said in a statement that one soldier also was missing as "forces have been engaging a large number of heavily armed terrorists" for the last two days. He did not say exactly where the fighting occurred but that about 20 people were arrested.
There was no independent confirmation of the military's claims.
Olukolade says the extremists are in "disarray" and fleeing to Nigeria's borders with Cameroon, Chad and Niger.
A decree by President Goodluck Jonathan put Adamawa, Borno and Yobe states under emergency rule, allowing the military to arrest anyone and occupy any building it suspects of housing extremists.