Justice Ranjana Desai and Justice R V More said in view of the importance of the case, they were also directing the State to ensure that Advocate General Ravi Kadam argues the matter himself.
The bench was hearing two petitions filed by lawyer V P Patil and former journalist Ketan Tirodkar seeking a CBI probe into Dey's killing.
The court also allowed applications filed by two journalist organisations -- Press Club, Mumbai and Marathi Patrakar Parishad -- to intervene in the matter as they also pleaded for a CBI probe into murder of Dey, who was shot dead by four unidentified assailants in suburban Powai on June 11.
Public prosecutor Pandurang Pol said investigations were on and the city police and its crime branch were moving in the right direction. He said the government was conscious and there was no need to transfer to probe to CBI at this stage.
However, the judges said they would like to know the progress made by city police and crime branch in the probe and asked the state to file a status report on June 21.
Petitioner Patil said, "Like fake encounters in the past, there was a possibility of fake investigations in this case" and pleaded for a probe by an independent agency like CBI.
Another petitioner, Ketan Tirodkar, argued that nexus between police and underworld was suspected and a CBI probe into Dey'' murder was justified.