"The 15- member delegation of journalists which met the Chief Minister demanded a CBI enquiry, but the demand was rejected," said Prasad Kathe, general secretary of Television Journalists'' Association.
Dey, investigative editor with Mid-Day, was shot dead in suburban Powai on June 11.
"We demanded that ordinance be passed regarding (proposed) law to prevent attacks on journalists. Chief Minister said he will put the draft before cabinet on June 15. Resignation from Home Minister R R Patil, and suspension of Mumbai Police Commissioner Arup Patnaik were another two demands, which were also rejected," he said.
However, Chavan assured the delegation that police had got some concrete evidence, and there would be a break-through within two days, Kathe said.
"We will wait till June 15... (if not satisfied) journalists will start a relay-hunger strike," he added.
"After a week, we will move the Bombay High Court and file a petition seeking CBI probe," he said.
Earlier, hundreds of journalists from print and electronic media participated in protest march from Patrakar Sangh to Mantralay.
The Chief Minister, who met the procession outside, said, "The state government is sensitive to the feelings of journalists and is doing whatever it can to bring the assailants to book," adding that he was personally monitoring the investigation.