Noting that police have been unable to nab the killers even a month later, the party, however, said it was willing to trust Home Minister R R Patil on his assurance that the probe was proceeding in the right direction.
"There is a demand being made to hand over the probe to CBI or NIA. This is akin to distrust shown in state police. "The demand to hand over the probe to CBI is foolish... what miracle will CBI or NIA do," an editorial in party mouthpiece Saamana said.
"Let state police probe the murder. We have full faith in our police," the editorial said.
It also attacked Chief Minister Prithviraj Chavan for "seeking to blame" right-wing Hindu Sanatan organisation for Dabholkar's murder.
While making no secret of their disappointment with the slow pace of investigations, Dabholkar's family has so far refrained from demanding a CBI inquiry into the killing.
"We still have faith in Pune Police and do not feel that a stage has come to demand a CBI inquiry," said Mukta, Dabholkars daughter and also an activist of the Andhshraddha Nirmulan Samiti (ANS), the anti-superstition group founded by the slain activist.
Interestingly, Maharashtra Navnirman Sena (MNS) chief Raj Thackeray on Thursday discounted the demand for CBI investigation while reposing trust in state police.
Narendra Dabholkar was shot dead by two unknown assailants in Pune.
The August 20 slaying of Dabholkar in Pune by two unknown assailants jolted the progressive social movement in Maharashtra.
Protest marches and dharnas marked the public ire throughout the state in the last few days as activists and his supporters gave vent to their anger and disappointment over the pace of investigation.