A bench headed by CJI SA Bobde said that there were enough safeguards to ensure fair inquiry by the judicial panel into the encounter which took place in Kanpur.
The commission will also probe the killing of eight policemen allegedly by Dubey's gang and the subsequent encounter of the gangster and five of his purported associates by the cops.
Vikas Dubey on July 2 had massacred eight policemen on duty and had brutally cut the circle officer's leg after shooting him dead.
Solicitor General Tushar Mehta, appearing for Uttar Pradesh, told the bench that he would file the status report by July 16.
The judicial commission which has been set up under the provisions of Inquiry Commission Act -1952 (Act number 60, 1952), will be headquartered in Kanpur.
A team of Juhu unit of Mumbai ATS arrested the duo from Kolshet in neighbouring Thane, he said.
The neutralised criminals were later identified as Atul Dubey and Prem Prakash Pandey. However, three others fled the spot.