The United Nations has condemned the army's campaign as ethnic cleansing. Until now, the military has maintained that it is carrying out legitimate counterinsurgency operations.
Many refugees start at transit centres set up along the Bangladesh-Myanmar border before they are brought to the main refugee camps in Cox's Bazar.
The 10 corpses were found in December 2016 in a mass grave near a cemetery in Inn Din village. The army appointed a senior officer to investigate.
The military claimed they had rushed to Inn Din to protect frightened Buddhist villagers and had been attacked by "200 Bengalis" with sticks and swords, 10 of whom were arrested and accused of having links to terrorists.
Ten of the attackers were captured after the security forces drove the rest off by firing into the air, according to the statement.
"We have chose to provide the aid in response to the agreement between Myanmar and Bangladesh to represent an global message of support so that the repatriation can be carried out promptly", said Foreign Ministry official Shinobu Yamaguchi in a statement.
"It was found that there were no conditions to transfer the 10 Bengali terrorists to the police station and so it was made a decision to kill them".
The villagers assisted in the execution, according to the statement, because they wanted revenge on the Rohingya militants who had killed their family members in the past.
A statement from the office of the commander-in-chief on Wednesday said the military's investigation had found that members of the security forces had killed the 10.
Anti-Rohingya sentiment is high not only among the military, but the general population, among whom a form of Buddhist nationalism has seen a resurgence since the end of military rule.
The military denied all accusations of significant human rights abuses in a report released in November following an investigation.
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".
Human rights groups have denounced systematic state sponsored violence against the religious group and ethnic minority, which includes mass murders, rape, laying landmines, and burning entire villages that has driven more than 655,000 Rohingya refugees into Bangladesh.