It says 37 people were killed, while others maintain at least 185 died.
The army says 30 members of the Boko Haram Islamist group, one soldier and six civilians died.
The Red Cross has backed local officials who say the figure is higher but they have not been into the town.
An army statement said three rocket-propelled grenade launchers had been recovered, along with bomb-making material.
The previous most deadly incident of the three-year Boko Haram uprising came last year when at least 160 people were killed in co-ordinated bomb attacks in the northern city of Kano.
The group is fighting to install Islamic law in the predominantly Muslim north of Nigeria.
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There are so many versions of what happened. Everyone tells his own version. So, no-one is sure which version to believe”
Isa LawanBaga MP
‘Military siege’
Baga is close to the border with both Chad and Niger and a multinational force from the three countries was attacked, its commander Brig Gen Austin Edokpaye said.
The Red Cross is still trying to gain access to the town to help those affected by the violence, national co-ordinator Umar Mariaga told the AFP news agency.
Local MP Isa Lawan told the BBC Hausa service that “what happened is Baga is sad and beyond description”.
“We have already started despatching relief materials, including building materials and food stuff. We want to make sure that people get the necessary assistance to start rebuilding their homes.”
He said there were “many versions of what happened. Everyone tells his own version. So no-one is sure which version to believe.
“Many people died. But the figure of casualties given by the people of Baga is 185.”
A resident who did not want to be named told AFP: