The authorities said their goal in gaining custody of the items was to set in motion the return of the stolen objects to India and their other countries of origin. Officials also hope to prosecute Mr. Kapoor, an American citizen, in the United States. Currently he is awaiting trial in India on charges of plundering archaeological sites and conspiring with black market traders to send illicit artifacts overseas. American officials are planning to extradite him after his case is settled.

Mr. Kapoor, whose defunct gallery, Art of the Past, sold hundreds of objects to prominent American museums and collectors, has denied any wrongdoing.

“At the present time we are at a distinct disadvantage because Mr. Kapoor is in an Indian jail and all the facts in this matter are known by him,” said Kenneth J. Kaplan, a lawyer for Mr. Kapoor. Manhattan prosecutors declined to comment on the case.

Since an initial raid on Mr. Kapoor’s gallery by Homeland Security Investigations agents in 2012, three of his associates have agreed to criminal penalties in exchange for cooperating with investigators, according to officials and lawyers. The case, which now extends to four continents and is being pursued in conjunction with Indian officials, has been named Operation Hidden Idol.