In a letter to the Prime Minister, CPI(M) General Secretary Prakash Karat and his CPI counterpart A B Bardhan said only such an inquiry can help bring out the "whole truth" about the 1995 incident.
"Recently, two of the persons involved in the affair, Niels Nielsen alias Kim Davy and Peter Bleach, have been talking to the media and providing information and making some allegations regarding the arms drop and how it was planned," the letter said.
"It is necessary to have a comprehensive probe into the whole affair. For this we request you to constitute a judicial enquiry by a sitting Supreme Court judge," it said.
The Left leaders said Davy, the prime accused in the case whose extradition to India has been sought by the CBI, has provided some "startling information" on how he was able to escape from the Mumbai airport after the plane which was involved in the airdrop was intercepted and asked to land there.
Though 16 years have elapsed and some of the accused were sentenced in the trial conducted in a Kolkata court, they said much remains to be "cleared up" about this incident which was a "serious assault" on the country's sovereignty and security.
"It concerns a conspiracy to unleash violence against the then elected government of West Bengal. It is also a case which had international ramifications along with the role of an organisation like the Ananda Marg, which was once banned by the Government of India," Karat and Bardhan said.