“I did not flee from India and neither am I an absconder“, Mallya said in a series of tweets posted on Friday.
Mallya also said that as a member of parliament he would fully comply with the law.
The Kingfisher baron left India last week, a lawyer for the lenders told the country’s top court on Thursday.
India’s finance minister has vowed to recover more than $1bn from the heavily indebted Mallya, as a political row erupted over his surprise departure.
Arun Jaitley told parliament that Mallya’s grounded Kingfisher Airlines owed a group of mostly state-run banks some 90 billion rupees ($1.34bn) in unpaid loans.
“The banks are taking all steps to recover every penny lent to him and they will recover it,” Jaitley said to jeers from opposition MPs.
“Before his passport could be seized, he had left the country,” the minister added.
The banks had asked the supreme court on Wednesday to prevent the 60-year-old quitting the country, but the attorney general said Mallya had already left on 2 March.
Mallya, who is thought to be in London, was given a $40m partial severance payment after stepping down last month as chairman of United Spirits, the Indian arm of Britain’s Diageo, following allegations of financial lapses.
The opposition Congress party demanded to know how Mallya was allowed to fly out when so many banks had taken legal action to try to claw back the debt.
“Why was Vijay Mallya not arrested?” Congress lawmaker Ghulam Nabi Azad asked in parliament.
The row risks embarrassing the Indian government and comes as state-run banks face growing pressure to step up recovery of a mountain of bad loans, which make them less able to lend to the corporate sector.
Reserve Bank of India governor Raghuram Rajan has ordered the banks to clean up their balance sheets by next March in efforts to boost the country’s economic growth.
Jaitley sought to blame the opposition, saying a string of banks granted the loans during the previous Congress-led government’s time in power.
Mallya was known as the “King of Good Times” before the 2012 collapse of his airline, which left thousands of workers unemployed and millions of dollars in unpaid bills.
As his liquor business flourished during the early 2000s, he diversified into other areas and in 2005 launched Kingfisher Airlines, named after his company’s best-known beer.
Once nicknamed “India’s Richard Branson”, he also acquired a stake in the Force India F1 team. His fortune reached a peak of $1.6bn in 2007, according to Forbes.
But he was unable to stop Kingfisher from haemorrhaging cash and the airline was grounded in 2012 having never made a profit.