Raising the issue in Rajya Sabha, D Raja (CPI) said Vijay had made the comment referring to developments in Chhattisgarh earlier this week.
"As a Communist, we don't need certificate from anyone," he said, adding the Left members had made immense contribution during the freedom struggle and had sacrificed their lives.
Deputy Chairman P J Kurien said the Chair had expunged those remarks.
Raja said expunging the remarks was not enough and the member should express regret. "How can you accuse Communists of terrorism... You cannot link Communism with terrorism," he said.
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Kurien said the remarks have already been expunged and the Chair cannot direct the member to apologise.
Vijay said he had great respect for Raja. "I have no intention to hurt anyone. We are ideologically poles apart," he said.
Refusing to apologise, he said he has worked in Left-wing extremism affected areas and Naxals say they are followers of Marxism-Leninism.
Kurien said the Chair cannot direct anyone to apologise but Chair will be happy if Vijay expresses regret.
Vijay, however, said he has nothing against the Left members but stopped short of expressing regret. "I have no intent to hurt you," he said.