Chennai journalists gathered at the Press Club to condemn the murder.
Past year she was found guilty of defaming a lawmaker from Modi's Bharatiya Janata Party (BJP) in a 2008 article about alleged corruption.
People say that the Prime Minister is quiet and he has not said anything.
"The CCTV camera has captured the whole incident", Indrajit, Lankesh's brother told reporters. But the entire idea is to crush dissent", Rahul said, adding that "non-violence is the history of this nation. "Murder can not be justified", he added.
"The intolerance unleashed on one pretext or the other appears to find tacit encouragement from the Union and State governments through its silence, thereby emboldening criminals to brazenly celebrate such crimes", it said in a statement. However, some in the party said it would tarnish the image of the Siddaramaiah government.
"The series of killings of rationalists, free thinkers and journalists has created an atmosphere that dissent, ideological differences and divergence of views can endanger our lives".
In Dharwad, just across Goa's border with Karnataka, where generations of Goans have studied and earned professional degrees, an organised protest began at the house of the late scholar M M Kalburgi, who was himself killed by mystery assailants in 2015. A joint memorandum, submitted to the Karnataka Chief Minister, sought speedy investigation and noted that the murder had sent "shock waves across the journalist community for its brazenness".
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It said the killings of Pansare, Dabholkar, Kalburgi and Gauri Lankesh "are all interconnected". She was critical of the Hindu right-wing forces.
Law Minister Ravi Shankar Prasad on Wednesday hit out those expressing happiness at the killing of activist-journalist Gauri Lankesh on social media.
Hear more about journalist Gauri Lankesh in The World's interview with Anoo Bhuyan above. She later particiapted in a silent march against the killing.
"The murder must be investigated effectively and with urgency", the All India Democratic Women's Association said in a statement.
"Baseless allegations are being levelled. It is unfortunate and not good for democracy", he said. He hoped that the Karnataka police would soon nab the killers.
The Minister accused Chief Minister Siddaramaiah of not taking previous sensitive criminal cases seriously.
The SIO Bhatkal unit in the presence of their unit president Zuhair SM and Secretary Abud Asif submitted an memorandum to the Governor of the state through Bhatkal Assistant commissioner (AC) demanding a quick and fair investigation of the case.