He said the moot question remains why was no action taken at that time in view of the knowledge of such situations in terms of allowing him to leave.
He said Mallya's claim is vindication of the party's stand and assertion that the government was always in the know about Mallya, Nirav Modi, Mehul Choksi and others who have fled the country.
Singhvi said the country wants to know what transpired during the meetings between Mallya and Jaitley.
"Today we have a categorical assertion by Mallya in UK about the number of times he met the finance minister to have some resolution of his dues with banks. The government should now explain how and why he was allowed to leave and what transpired at those meetings. The nation wants to know," he said.
Singhvi said the Congress has repeatedly asserted for the past over 18 months that not only Vijay Mallya, but also Nirav Modi, Choksi and many others have been allowed to leave the country with impunity.
He said the phrase used by Mallya that 'I met the finance minister' does not suggest a passing and casual meeting inside Rajya Sabha. "I think more categorical and detailed response must be had. Question remains how could he have left after everyone knew of debts and NPAs," he said.
The Congress also tweeted on its official handle, saying, "Vijay Mallya met FM Arun Jaitley several times before escaping the country to discuss a settlement plan, in spite of this the BJP government allowed him to flee with thousands of crores debt. Do we need anymore proof that this govt. is in the pocket of crony capitalists."
Congress chief spokesperson Randeep Surjewala said that with Mallya's revelation one thing is clear that the BJP is running "a travel, tour and immigration agency for looters to settle abroad".
"After Mallya reveals his 'consultation meetings' before his smooth escape...one thing is clear...BJP is running tour, travels and immigration agency for loot, scoot and settle abroad brigade," Surjewala said.
In a swipe at the government's 'sabka saath, sabka vikas' slogan, the Congress leader said the BJP's sole aim now was 'Bhagode ka saath, Lootero ka vikas' (helping absconders and enriching looters).
"Vijay Mallya left India with the country's money after a farewell from Arun Jaitley. Chowkidaar nahin, Bhagidaar hai (Not a watchman, but a partner)," he tweeted in Hindi.
Another Congress leader Anand Sharma said, "Vijay Mallya has run away after looting money from banks. Government had this information. So, when Finance Minister gave statements in Parliament on Vijay Mallya issue, he should have mentioned about this meeting with Mallya. Only FM can tell why he didn't tell about it?"
Earlier, the 62-year-old former Kingfisher Airlines boss told reporters in London that he met the minister and offered to settle with the banks.
"I left India because I had a scheduled meeting in Geneva. Before leaving I met the finance minister and offered to settle (the issue with the banks), Mallya said, without naming the minister. He is facing court proceedings in London where India's plea for his extradition is being heard.