Mr Gogoi asked state Additional Chief Secretary V.B. Pyarelal to carry out the inquiry and submit the report within 30 days.
The incident took place early on Wednesday at Raijungbari village in Runikhata, about 200 km from Assam's main city Guwahati.
Police and army personnel killed two youths and injured another. They said the two slain youths were cadres of the anti-talk faction of the National Democratic Front of Bodoland (NDFB) led by I.K. Songbijit.
One AK-46 rifle, one grenade and 15 rounds of live ammunition were recovered from their possession. Police said the injured youth was a linkman of the outfit.
Residents, however, said the three boys were from the same family and that they were innocent. The slain youths - Jiri Narzary and Pranjit Narzary - were students of Class 7 and 10 while the injured Nikedin Narzary is a student of Class 6 in a local school.
Residents on Wednesday came out on the streets to protest the killings, attacked the Runikhata police station and also set fire to some motorcycles.
This forced police to resort to a baton charge and fire blank rounds to disperse the crowd. The Chirang deputy commissioner also ordered a magisterial inquiry into the incident.