Gandhi alleged Goa minister Vishwajit Rane is heard in the audio clip saying that Parrikar, a former defence minister, had told his cabinet during a meeting that all documents relating to the Rafale deal were with him.
"I would like to debate with the Prime Minister one-on-one on Rafale, on anything on combat aircraft. Just give me 20 minutes," said Gandhi demanding Modi to answer "credibly" questions raised by him about the deal to procure 36 fighter jets from France.
He said he had asked the prime minister to explain why an amount of Rs 1,600 crore was paid for each aircraft instead of Rs 560 crore and why the contract was given to "AA", an abbreviation used for Reliance Group's Anil Ambani, and not the public sector Hindustan Aeronautics Limited (HAL).
"Tomorrow, the PM faces an Open Book Rafale Deal Exam in Parliament.
"Here are the exam questions in advance: Q1. Why 36 aircraft, instead of the 126 the IAF needed? Q2. Why 1,600 Cr instead of 560 Cr per aircraft. Q4. Why AA instead of HAL? Will he show up? Or send a proxy?" the Congress chief said on Twitter.
He also accused Finance Minister Arun Jaitley of lying about the deal. "The decision is on Rafale and the decision maker who announced the deal with pomp is not answering and Jaitley is trying to defend Modi and his actions.
"Modi can run away from debate, but the truth cannot be hidden. The entire country knows that Modi changed the deal to help his industrialist crony pocket Rs 30,000 crore," alleged Gandhi.
Gandhi, while speaking in the Lok Sabha, said Modi "does not have guts" to come to Parliament and confront questions on the Rafale deal.
(With inputs from IANS and PTI)