Launching a scathing attack on NDA government, Left parties demanded immediate release of Kumar and other leaders of Left-backed outfits and a stop to "illegal and uncalled for action by Delhi Police".
The parties said they will take up the issue with Union Home Ministry and also during budget session of Parliament.
"The question is do you know who raised the slogans? Take action according to law against them. When you don't know, then how are you arresting all the student leaders?
Yechury claimed the FIR against Kumar and others does not contain any name and sought to know on what basis the alleged raid was conducted "in the name of anti-national activities".
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In its Facebook post, the CPI(M) accused Modi government of resorting to "totally dictatorial" measures to "crush" Left-backed students' organisations and promote pro-RSS organisation in campuses "as was done" in Hyderabad Central University, which the party said, was "shameful".
Deploring the police action, CPI general secretary S
Sudhakar Reddy insisted that police first "ascertain facts" and demanded "immediate" release of Kumar and others.
"CPI demands the immediate release of Kumar and other leaders and withdraw police from university campus," he said.
Meanwhile, party national secretary D Raja visited the campus to express solidarity with agitating students and also met Vice Chancellor Jagdeesh Kumar and registrar Bhuprendra Zutshi in this regard.
Addressing the protesters there, Raja said the CPI will take up the issue with the Home Ministry and also during upcoming budget session of Parliament.
The CPI(M) Politburo has demanded immediate release of JNU students who have been arrested and ordering of an independent inquiry.
"We strongly condemn the indiscriminate arrests of Left and progressive student leaders from JNU campus. We demand immediate release of those who have been arrested and ordering of a proper independent inquiry under the due process. The university authority must also stop such illegal and uncalled for action by Delhi Police," the CPI(M) politburo said in a statement.
"An isolated incident, which does not reflect the opinion of the vast majority of the students, is now being blatantly used as an excuse to clamp down on the progressive and democratic student movement. This has been a long harboured design of the RSS and its camp followers.
It noted that for nearly half a century the student movement in JNU has had the "impeccable record of upholding the unity and integrity of the country and rising in protests against any expression of anti-national terrorist activities.