Soldiers had also killed a man who featured in Boko Haram's propaganda videos pretending to be the group's leader Abubakar Shekau, it added.
Last year, the military said that Shekau may have been killed, without providing any proof.
Boko Haram has suffered heavy losses in recent weeks in battles in its stronghold of north-eastern Nigeria.
The military said that 135 Boko Haram members surrendered with their weapons in Biu, Borno state, on Tuesday - and that 133 others surrendered elsewhere in north-eastern Nigeria.
The BBC's Will Ross in Lagos says that the claims are impossible to verify.
However, if they are true, it could be a major turning point for the army's campaign against Boko Haram militants, our correspondent adds.
General Chris Olukolade of the Nigerian military said that a man named Mohammed Bashir was among those killed in the latest offensive against Boko Haram last week.
Bashir "had been acting or posing in videos as the deceased Abubakar Shekau, the eccentric character known as leader of the group", he said.
Gen Olukolade did not give further details.
In a statement in August 2013, the military said intelligence reports indicated that Shekau "may have died" in a shoot-out with government forces at a Boko Haram camp in the vast Sambisa Forest, along Nigeria's border with Cameroon, about two months earlier.
But Nigerian journalist Ahmad Salkida, who has good contacts in Boko Haram, says on on his Twitter account that he has it "on authority that Shekau is well and alive".
He said he met Shekau during a failed attempt to negotiate the release of 200 schoolgirls who were abducted by Boko Haram in April.
Who are Boko Haram?
Who are Boko Haram?
Profile: Boko Haram leader Abubakar Shekau
Since the abduction, which caused international outrage, a man purporting to be Shekau has appeared in videos, taunting the military and declaring the establishment of a caliphate in areas controlled by Boko Haram.
Speaking at the United Nations Security Council meeting, Nigerian President Goodluck Jonathan urged the council to find more ways to combat the militant threat.
"Evidence has shown that Boko Haram is sourced largely from outside our country," he said.
"Only by united action and firm resolve can we check this urgent threat to humanity and also build the enduring structures that will resist their re-emergence."
"Boko Haram" means "Western education is forbidden" in Arabic, and the group frequently attacks schools and colleges, which it sees as a symbol of Western culture.
The New York-based Human Rights Watch says more than 2,000 civilians have been killed in the region this year.

In court last year Christopher Anthony admitted damaging the Grade II-listed building during work in 2008.
The judge ruled Mr Anthony could not afford to pay the council's legal bill but gave permission for the issue to be revisited within a certain time frame.
Officials have now said Mr Anthony's circumstances have not changed and the order had been allowed to lapse.
The Hippodrome has been derelict for some years when much of the roof and part of the exterior walls collapsed in 2008.
In April 2010 developer Mr Anthony, of Bishops Stortford, was given a conditional discharge after admitting ordering work on the building without permission.
Since then the council has carried out £43,000 worth of stabilisation work on the structure.
A spokesman said: "Derby City Council intends to recover the cost of the works carried out on Macklin Street and we are reviewing Mr Anthony's financial circumstances to assess the available options."
More than 260 Islamist militants have surrendered in north-eastern Nigeria, the military has said.
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Derby City Council has decided not to pursue the owner of the Hippodrome Theatre for £17,000 in legal costs.