The police said soon after Kumar's car reached Mahajati Sadan, the venue of the convention jointly organised by AISF and AIYF (All India Youth Federation), the BJP workers started throwing rotten eggs at him while shouting slogans.
They condemned Kumar for his "anti-national" activities.
Amidst tight security, Kumar, who is also the president of JNU Students' Union (JNUSU), was somehow taken inside the Mahajati Sadan auditorium in north Kolkata.
Ten demonstrators, including three women, were arrested, the police said.
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Speaking at the convention, Kumar flayed the Centre's intolerance, referring to Dalit research scholar Rohith Vemula's death in Hyderabad.
He said, "Those who are responsible for the death of Vemula have nothing to defend themselves. The government should protect its people as human beings and not on the basis of their religion, caste or creed."
The programme was held amid tight security and considerable police deployment.
One of the organisers claimed that the BJP staged the demonstration "out of fear".