"We will set up a special team to investigate the incident", said the official.
Gadkari sought to put the onus of maintaining law and order on the Congress government in Karnataka.
This came after Home Minister Rajnath Singh directed Home Secretary Rajiv Gauba to get a report from the state government.
Following the murder of Gauri near her residence in Bengaluru on Tuesday, several journalists, thinkers and activists expresses outraged at the killing of the 55 year old journalist.
Gauri, a writer, publisher and editor, had returned home in her vehicle and was opening the gate when motorcycle-borne assailants sprayed bullets, with two hitting her on the chest and one on her forehead.
"We want an impartial investigation based on circumstantial evidences".
Press Club of Bengaluru president Sadashiva Shenoy, who was closely associated with Gauri, said, "divisive forces can not muzzle the liberal voices by resorting to killing".
Gauri was the editor of the Gauri Lankesh Patrike, a tabloid described as an "anti-establishment" publication.
After the murder of Gauri, some members of Pansare family joined the protest rally in Delhi on Wednesday.
Journalists took out a march from the Press Club in Bengaluru to the Vidhana Soudha, the state secretariat, and submitted a memorandum to Chief Minister Siddaramaiah seeking immediate action to bring the culprits to book. "These killings are a threat to democracy and I appeal to everyone to unite and fight against radical and fascist Hindutva ideology which has paralyzed the entire country", said Pappu Dutta.
Star Wars Episode 9 director quits
Superman helmer Zack Snyder and enigmatic Twin Peaks director David Lynch, who turned down Return of the Jedi (1983). Rey ( Daisy Ridley ) is at the center of Star Wars: The Force Awakens , The Last Jedi and, presumably, Episode IX .