LONDON — Nirav Modi, whose opulent necklaces have been worn by A-list celebrities, was in custody in London after being denied bail following his arrest this week in a bank fraud in India totaling nearly $3 billion.

The Indian government wants to extradite Mr. Modi from Britain to face charges that he, his family and business associates assembled a global empire with money obtained illegally, mostly from government-run banks.

Mr. Modi, whom the authorities had sought since early last year, was arrested in central London on Tuesday after trying to open a bank account, according to news reports.

Mr. Modi’s lawyer, George Hepburne Scott, said at a bail hearing on Wednesday that Mr. Modi had been living lawfully in London since before the allegations were made last year, according to Reuters. But the district judge, Marie Mallon, was not persuaded and denied bail.