The move came after Home Minister Rajnath Singh directed Home Secretary Rajiv Gauba to get a report from the state government, the home ministry official said.
The Karnataka government has been asked to provide details of the incident and the steps taken to nab those involved in the killing, the official said.
The 55-year-old journalist, known for her outspoken views on Hindutva politics, was gunned down at her residence in Bengaluru yesterday.
The Karnataka government today decided to form a Special Investigation Team to probe the killing.
Information and Broadcasting Minister Smriti Irani condemned the killing of Ms Lankesh and hoped there would be a speedy investigation and justice delivered.
Congress president Sonia Gandhi and vice president Rahul Gandhi also condemned the incident. While Mrs Gandhi said it was a chilling reminder that "intolerance and bigotry is raising its ugly head in our society", Rahul Gandhi expressed shock and said no one could suppress the truth.
The Editors Guild of India "strongly condemned" the murder of Ms Lankesh and called for a judicial probe into the incident.
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