U.S. agents have arrested two relatives of Venezuelan President Nicolás Maduro on charges they conspired to transport 800 kilograms of cocaine to the U.S., according to two people familiar with the matter.

The arrests come amid U.S. accusations that the top echelon of the government in Caracas is involved in the narcotics trade.

The two men, Efraín Antonio Campo Flores and Francisco Flores de Freitas, were first arrested in Port-au-Prince, Haiti, on Tuesday by local police, turned over to U.S. Drug Enforcement Administration agents and flown the same day to New York in a DEA jet, these people said. The two were scheduled to go before a federal judge in New York on Thursday, they said. A spokesman for the federal district court declined to comment.

Mr. Campo Flores, 29 years old, identified himself on the DEA plane as a stepson of the president, according to the people familiar with the matter, having been raised by his aunt, Cilia Flores, who is Mr. Maduro’s wife. A U.S. document said the other man identified himself as a nephew of Ms. Flores.

Ms. Flores, 62 years old, is one of the most powerful figures in Venezuela’s government. The longtime partner of Mr. Maduro, she married him in July 2013 after his election as president.