Dozens more were suspected to have lost their lives in the attack on the base in Metele village, in Borno state near the border with Niger, although numbers have not been confirmed.
President Muhammadu Buhari made defeating the Islamist insurgents a key plank of his 2015 election campaign and has said the jihadists were “technically defeated”.
But that claim has been called into question by repeated attacks, including suicide bombings and raids targeting civilians and the military.
Neither the government nor the military has commented on the latest deaths, which were claimed by the IS-backed Boko Haram faction, the Islamic State West Africa Province.
But Buhari’s main challenger at next February’s election, Atiku Abubakar of the Peoples Democratic Party, sent a condolence message to the families of those who were killed.
He was also reported as saying on Friday that the losses were “a clear sign that our troops need to be better funded and better equipped”.
On Thursday night, Senate leader Bukola Saraki, a Buhari critic who defected from the ruling All Progressives Congress to the PDP earlier this year, also spoke out about the deaths.
He also announced that a delegation of senators would travel to the northeast to visit front line troops, as others in the party questioned the effectiveness of the counter-insurgency.
“It is time that we face the reality that Boko Haram is not technically defeated,” said Peter Ayodele Fayose, a former state governor and leading PDP figure.
More than 27,000 people have been killed in nine years of fighting and 1.8 million others are still homeless, as aid agencies tackle the humanitarian fall-out from the conflict.
Amaechi Nwokolo, a security analyst at the Roman Institute of Security Studies in Abuja, told AFP: “The whole thing (the insurgency) has been politicised.
“Now, as election season and Christmas approach, we are likely to see an upsurge in attacks. These terrorists are not dumb. They will certainly want to create chaos around the election.”
Political analyst Chris Ngwodo said the PDP would likely want to make capital out of the current situation but added it had not translated into a loss of support for Buhari or the APC.
“I can’t see that these attacks have shifted public opinion here,” he said from the Borno state capital, Maiduguri. “Borno still feels like Buhari territory.
“The opposition will look for chinks in the armour of the ruling party but I don’t know if they can generate the kind of traction from these kinds of incidents.”