A number of chief ministers as well as Union ministers also expressed outrage at the killing of the 55-year-old senior journalist, known for her strong views against right- wing forces.
As Lankesh's murder last evening outside her residence in Bengaluru triggered waves of spontaneous protests across the country by journalists and civil rights groups, the Union Home ministry sought a report from the Karnataka government on the killing.
"It is an extremely sad moment for our democracy and a chilling reminder of the fact that intolerance and bigotry is raising its ugly head in our society," Gandhi said.
Congress vice president Rahul Gandhi said anybody who spoke against the ideology of the BJP and RSS was "pressured, beaten, attacked and even killed".
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The comments drew a sharp reaction from the BJP which accused Rahul of trying to make "political capital" out of Lankesh's murder and rejected as "irresponsible and baseless" the allegations linking the killing to the people following its ideology.
"The government, the BJP or any of its organisations have no connection with the killing of journalist Gauri Lankesh," Union minister and senior BJP leader Nitin Gadkari told reporters.
Sonia and Rahul Gandhi spoke to Karnataka Chief Minister Siddaramaiah and urged him to swiftly bring the culprits to book.
The CPI(M) also expressed shock over the killing, alleging that it fit into the "familiar pattern of eliminating voices that dare to speak against the climate of intolerance by the RSS and BJP".
Condemning the murder, AAP expressed the fear that its leader and former scribe Ashish Khetan could meet a similar fate for taking on right-wing elements.
The chief ministers of Punjab, West Bengal and several other states also condemned the killing.
Lankesh, the editor of Lankesh Patrike, had returned home in her car and was opening the gate to her house when the assailants on a motorcycle fired at her indiscriminately. Two bullets hit her on the chest and one on her forehead, police officials said in Bengaluru.