A special court in Mumbai on Monday ordered the arrest of Mallya, days after government suspended his passport in a bid to force his return from abroad and make him repay dues.
Jaitley said he would not comment on court proceedings.
"You have investigative agencies looking into criminal law matters (and) you have banks looking into settlement matters. I think both are extremely competent institutions who can act strictly within the parameters of law," he told ET Now.
"As far as the banks are concerned, its their responsibility based on commercial considerations to make sure that no defaulter manages to get away," Jaitley said. "Merely by escaping the geographical boundaries of India you don't run away from the liabilities that you owe to the public system."
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The Supreme Court has asked Mallya to declare all his assets by April 21 after a group of lenders turned down his proposal to repay as much as USD 900 million.
Mallya has previously termed shutting down of Kingfisher Airlines as an "unfortunate commercial failure" due to macroeconomic factors and government policies. He said he did not flee the country and was not an "absconder."
"They (investigating agencies and banks) are sending a very strong signal that public debts owed to commercial banks, you cant just run away from liability if you have responsibility to pay and banks will ensure that banks are reimbursed," Jaitley added.