The teenagers died after soldiers fired at a car on the outskirts of Srinagar on Monday, while another youngster was critically wounded.
"We take responsibility for the death of the two boys in Kashmir," the chief of the army's northern command, D S Hooda, told reporters in Srinagar late Friday in televised remarks.
"We admit a mistake was made...there was some information about a white car with terrorists. Obviously, the identity was mistaken in this case," the Lieutenant General added.
Hooda promised an investigation into the deaths that would be conducted employing "the highest standard of transparency".
Yesterday, the army decided to shift the company of 53 Rashtriya Rifles (RR) from the area, which is a counter-insurgency force deployed in Indian Kashmir by the Indian Army.
Kashmir has been divided between India and Pakistan since independence from British colonial rule in 1947, but both claim the scenic Himalayan region in full.
Tens of thousands of people, most of them civilians, have died in fighting between Indian forces and a dozen rebel groups seeking independence or a merger of the territory with Pakistan.
Kashmir is still reeling from devastating floods in September that killed more than 200 people and destroyed public infrastructure and businesses.
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Admitting a mistake is a good sign - doesn't happen often in the Kashmir conflict.
It is commendable on the part of the General officer Commanding to admit that mistake had been committed before the completion of army's court of inquiry. Despite this being case of mistaken identity, loss of two precious lives is indeed regrettable which in future should be avoided at all cost.
Killing is a mistake.First time got to know.Why people in India are not protesting like they did at the time of Delhi Girl rape.Wrong is Wrong and right is right.Who did it should be punished and this applies in Pakistan also.The Justice for Christians killed.Why we are not protesting...World of hypocrites....