While interacting with media, Indrajit said: "We want justice. We cannot wait for two years to get justice like it happened in case of other activists."
Gauri's sister Kavita taking Indrajit into confidence, said Karnataka Chief Minister Siddaramaiah has taken initiative in the case so they want to wait for the probe to take place.
The Karnataka government has decided to constitute a Special Investigation Team (SIT) to probe the case.
Gauri's 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 Gauri 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.
Gauri's 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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