Bharatiya Janata Party national vice-president Dinesh Sharma also questioned the silence of the West Bengal's ruling Trinamool Congress.
Calling for punishment for the students who participated in the "anti-India" march, the BJP on Saturday said the CPI-M and the Congress should drop India from their party names for supporting "anti-nationals".
Interacting with media persons, Bharatiya Janata Party national vice-president Dinesh Sharma also questioned the silence of the West Bengal's ruling Trinamool Congress over a section of JNU students holding a meet on Tuesday to mourn hanging of parliament attack convict Afzal Guru and Jammu Kashmir Liberation Front (JKLF) co-founder Maqbool Bhat.
"When the whole country is outraged at the protesters who publicly gave anti-India slogans and supported a terrorist like Afzal Guru, the Communist Party of India-Marxist and the Indian National Congress, instead of condemning, have been rallying in their support," he said.
Mr Sharma strongly criticised CPI-M general secretary Sitaram Yechuri who on the day met union Home Minister Rajnath Singh demanding the release of JNU students' union president Kanhaiya Kumar arrested on sedition charges.
"What can be more unfortunate than people are now advocating for those who deserve strong action for their anti-national stand.
"Both Congress and CPI-M who are supporting such anti-national elements, should drop India from their party names because they are pursuing anti-national politics. They are as guilty as the protesters," said the BJP leader.
Questioning the the Trinamool's silence over the issue, Mr Sharma said: "The silence itself is an indication of their support to such anti-India sentiments. The Trinamool is no different from the Congress or the CPI-M.
"The protesters deserve to be punished for their anti-national stand and parties cutting across political lines should condemn it but unfortunately many of them are indulging in politics," he alleged.