The military responded with "clearing operations" that rights groups say have been accompanied by rapes and murders of Rohingya civilians whose houses have been burned down.
Myanmar's military hasn't made a public admission of guilt until now.
Ten of the assailants were captured, but "it was found that there were no conditions to transfer the 10 Bengali terrorists to the police station and so it was chose to kill them", the military said, and vowed to take action against those involved in the killing.
"However, it is only the tip of the iceberg and warrants serious independent investigation into what other atrocities were committed amid the ethnic cleansing campaign that has forced out more than 655,000 Rohingya from Rakhine State in August", he added.
Myanmar contends that the operations are legitimate counterinsurgency measures in response to attacks by Rohingya militants on border guard posts in August.
Two Reuters journalists who were also investigating the incident were arrested last month for allegedly acquiring "important secret papers" from two police officers.
Soldiers and villagers were involved in the killings of "Bengali terrorists" and legal action would be taken against them, said the statement on the Facebook page of Min Aung Hlaing, the military's commander-in-chief, quotes Al-Jazeera.
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"Action will be taken against the villagers ... and the security force members who violated the rules of engagement according to the law", the statement said.
Myanmar's Defense Ministry Information office released a statement Wednesday stating its forces had killed 10 suspected terrorists whose remains were found in a mass grave in Inn Din village of Maung Daw Township in the Northern Rakhine State.
The head of Myanmar's government and Nobel Peace Prize-winner Aung San Suu Kyi has failed to recognize the crimes committed against the Rohingya people, denying charges of "ethnic cleansing".
Ten of the attackers were captured after the security forces drove the rest off by firing into the air, according to the statement on Facebook, which the military often uses to make announcements. In a statement, the military said that due to the fighting they could not transport the men so the detainees were executed by soldiers and local villagers instead of being handed over to police. According to the statement, there were "no conditions" to hand the ten captured "bengali terrorists" over to the police, so "it was chose to kill them".
The military investigation was led by Lt Gen Aye Win.
In a December letter to the Bangladesh and Myanmar governments, Human Rights Watch warned that they risk violating global law by pressuring refugees to return to Myanmar where they are still at risk of attack by security forces.
James Gomez, Amnesty International's Southeast Asia and Pacific director, said the acknowledgement marked "a sharp departure from the army's policy of blanket denial of any wrongdoing".