The party also described as "hypocritical" the Centre's announcement to conduct a judicial probe into the suicide of Rohith Vemula and the decision to revoke the suspension of four other Dalit scholars from Hyderabad University.
"Continuance of Dattatreya and Irani as ministers in the Union Cabinet is untenable. Modi should realise if his government has to salvage some of the moral authority it has lost, they have to go," former CPI(M) general secretary Prakash Karat said, adding the varsity's Vice-Chancellor should also be removed.
The CPI(M) leader said the way the two ministers countered the charges against them only highlighted their "culpability" in the matter and "hostility" to Dalit aspirations for equality and social justice.
He noted the government changed its "brazen" stance to announce a judicial probe into the matter and revoked the suspension of the four students only after witnessing "widespread" outrage over Rohith's suicide.
"Modi, faced with protests in the Ambedkar Law University in Lucknow, talked of loss of a son of Mother India. But these are all hypocritical responses and will not do.