A division bench comprising Chief Justice D Y Chandrachud and Justice Dilip Gupta, after a perusal of the report which was submitted in a sealed cover, fixed August 5 as the next date of hearing.
The court had sought CBI's progress report while hearing a petition filed by NGO Stree Mukti Sangathan.
The petition, which had been filed before the Uttar Pradesh government's announcement of a CBI inquiry, alleged that state agencies would not be able to conduct a free and fair probe and had demanded that the investigation be handed over to the central agency.
Two teenage girls, both of them cousins, had gone missing from their house in Katra Sadatganj village of Badaun district on May 27 and their bodies were found hanging from a tree a day later.
Sexual assault was confirmed in the post-mortem examination. The case evoked a huge outcry and the ruling Samajwadi Party came under attack from all opposition parties. The court had stated on June 11 that it would monitor the investigation into the case.