U.S. prosecutors are investigating several high-ranking Venezuelan officials, including the president of the country’s congress, on suspicion that they have turned the country into a global hub for cocaine trafficking and money laundering, according to more than a dozen people familiar with the probes.

An elite unit of the Drug Enforcement Administration in Washington and federal prosecutors in New York and Miami are building cases using evidence provided by former cocaine traffickers, informants who were once close to top Venezuelan officials and defectors from the Venezuelan military, these people say.

A leading target, according to a Justice Department official and other American authorities, is National Assembly President Diosdado Cabello, considered the country’s second most-powerful man.

“There is extensive evidence to justify that he is one of the heads, if not the head, of the cartel,” said the Justice Department official, speaking of a group of military officers and top officials suspected of being involved in the drug trade. “He certainly is a main target.”

Representatives of Mr. Cabello and other officials didn’t return phone calls and emails requesting comment. In the past, Venezuelan authorities have rejected allegations of high-ranking involvement in the drug trade as an attempt by the U.S. to destabilize the leftist government in Caracas.

In an appearance on state television Wednesday, Mr. Cabello said he solicited a court-ordered travel ban on 22 executives and journalists from three Venezuelan news outlets that he has sued for publishing stories about the drug allegations earlier this year. “They accuse me of being a drug trafficker without a single piece of evidence and now I’m the bad guy,” Mr. Cabello said. “I feel offended, and none of them even said they’re sorry.”