The constable is alleged to have been killed by his colleague, Special Police Officer Eijaz Ahmed, to avenge his "sexual assault".
A vacation bench of justices D Y Chandrachud and S K Kaul asked the state Director General of Police to file a fresh status report and posted the matter for further hearing on July 17.
The apex court was not satisfied with the status report filed today and sought a detailed and comprehensive report.
Bhat's body was recovered after 21 days on June 7.
The apex court had on June 8, issued notice to the Centre and the Jammu and Kashmir Police on the plea of Pandita, who also hails from Kupwara and sought the status report on the investigation.
Pandita alleged DIG Ghulam Hassan Bhat on May 31 had came out with a version saying that the SPO had allegedly confessed to killing Sameer as the latter had sexually assaulted him on May 13.