The party also said the Supreme Court should institute a Special Investigation Team (SIT) into the matter.
"The CPI demands that the government release white papers about the enquiry along with the names of Panama leaks and Paradise Papers. The Supreme Court should institute an SIT to enquire into the black money in foreign banks," party general secretary S Sudhakar Reddy said in a statement.
The government said yesterday a multi-agency group probing the Panama Papers leak would also take "swift action" on the Paradise Papers on financial holdings abroad that list a number of Indian entities.
The party, which had earlier written to Prime Minister Narendra Modi demanding a white paper be issued on the Panama Papers leak, said, "The release of the list of black money holders by the Paradise Papers including 714 Indian nationals exposed the bankruptcy of the Indian government sponsored investigations into black money."
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Reddy accused the government of "defending some VVIP black money holders from getting exposed by not releasing their names and keeping them as top secret in sealed covers".
The Paradise Papers relate to an investigation into offshore and banking assets of individuals and entities carried out by the Indian Express in collaboration with the International Consortium of Investigative Journalists.