The top court said the filing of FIRs has served the purpose of the petition filed by the protesting women wrestlers and seven of the complainants have been provided adequate security.
The court has instructed the wrestlers to approach the judicial magistrate court or high court for further action.
The bench, led by Chief Justice of India DY Chandrachud, went through the status report of the case.
Earlier, women wrestlers had filed a plea seeking action against Singh for allegedly harassing them sexually.
Advocate Hooda, who represents the wrestlers, stated that on April 21, the complainants had reached the police station, but it took two hours for the cops to give a receipt of the complaint.
Solicitor General (SG) for the Delhi Police argued that there were seven complaints, and it takes time to register.
However, Hooda countered that it took them three hours to give a receipt of the complaint, and they did not register the FIR on April 21.
Finally, the FIR was registered on April 28, after the matter came to court.
The wrestlers have demanded an impartial investigation into the matter and have called for Singh's removal from his position as the WFI chief.