LONDON — Michael Kors said on Tuesday that it would buy Versace, the Italian fashion house, for $2.1 billion in a bid to challenge Europe’s conglomerates at a time of rapid consolidation in the global luxury market.

The deal, which would end the independence of one of the last prominent stand-alone fashion brands, is the biggest effort yet by Kors to build an empire. To reflect its growing collection of trophy brands, Kors said, the company will change its name to Capri Holdings Limited once the deal is completed.

Kors described the purchase as a milestone in its expansion plans. The Michael Kors brand had its roots in the “middle market” of the luxury sector and relied on outlets and department stores, where deep discounting is common. But mall traffic has declined in North America — Kors’s biggest market — and shoppers were changing, too, increasingly seeking brands at the extreme of the style and price spectrum.

Acquiring Versace, led by the artistic director Donatella Versace, whose flamboyant gowns can sell for thousands of dollars, is part of the company’s strategy to woo more big spenders — and find more loyal customers in Europe and Asia. Last year, Kors bought the shoe designer Jimmy Choo for 896 million pounds, or $1.2 billion at current exchange rates.