The flamboyant Indian liquor and aviation tycoon, 61, was first arrested by British police on behalf of the Indian authorities in April.
He was rearrested on Tuesday after India laid new charges against him.
India is seeking Mallya's extradition over loans to him tied to his defunct Kingfisher Airlines after the businessman, co-owner of the Force India team, moved to Britain in March last year.
Banks want to recover about $1.4 billion that the Indian authorities say Kingfisher owes.
Launching new extradition proceedings at London's Westminster magistrates court, Mark Summers, the lawyer representing the Indian government, said the original allegations related to fraudulently obtaining and misusing funds.
The new charges concerned the distribution of those funds, Summers said.
"The government alleges for example some of the funds have ended up with the Force India Formula One team," he said.
Mallya, wearing a blue jacket and open-necked white shirt, denies any wrongdoing and said he did not consent to being extradited.
He was released on police bail and declined to comment after the short hearing.
The next hearing in his case will take place on Nov 20 with a full eight-day extradition hearing due to start on Dec 4.
The judge will then make a decision based on whether there is a prima facie case against Mallya and whether the alleged crimes would be offences in Britain as well as India.
That ruling can be challenged in a higher court before being passed to the Home Secretary (interior minister) for approval. The minister's decision can also be appealed to the courts.