The SIT has been formed by the Karnataka government.
Gauri Lankesh's murder has sparked country-wide protests.
Her family also said they will move to the Central Bureau of Investigation (CBI) if they fail to get any justice in the murder case, media reports said.
However, the police could not identify the gunmen who killed the journalist-activist by examining CCTV footage.
Lankesh, a popular journalist who took stand against Right-wing ideology, was shot three times by some unknown assailants outside her residence.
Her murder bears a resemblance with earlier murders of rationalists Narendra Dabholkar and MM Kalburgi.
Her brother Indrajit Lankesh told reporters that one lady who stays opposite his sister's house heard the noise of the shooting first which she initially mistook it as fire crackers and later identified Gauri's body lying down.
Lankesh, who worked as an editor in a Kannada weekly Lankesh Patrikewas, died at an age of 55.
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