A top Venezuelan official declared on Sunday that the country's government would stay unified behind President Nicolas Maduro, whose capture by the United States has sparked deep uncertainty about what is next for the oil-rich South American nation.

Maduro is in a New York detention centre awaiting a Monday court appearance on drug charges.

US President Donald Trump, who went golfing on Sunday, ordered his seizure from Venezuela on Saturday and said the US would take control of the country.

But in Caracas, top officials in Maduro's government, who have called the detentions of Maduro and his wife Cilia Flores a kidnapping, were still in charge.

"Here, the unity of the revolutionary force is more than guaranteed, and here there is only one president, whose name is Nicolas Maduro Moros. Let no one fall for the enemy’s provocations," Interior Minister Diosdado Cabello said in an audio recording released by the ruling PSUV socialist party.

Images of the 63-year-old Maduro blindfolded and handcuffed on Saturday stunned Venezuelans.

The operation was Washington's most controversial intervention in Latin America since the invasion of Panama 37 years ago.

Without providing specifics, Defence Minister General Vladimir Padrino said on state television the US attack killed soldiers, civilians and a "large part" of Maduro's security detail "in cold blood."

Venezuela’s armed forces have been activated to guarantee sovereignty, he said.

Vice President Delcy Rodriguez – who also serves as oil minister – has taken over as interim leader with the blessing of Venezuela's top court, though she has said Maduro remains president.

She has also publicly contradicted Trump's claim she is willing to work with the United States.

Trump said Rodriguez may pay a bigger price than Maduro "if she doesn't do what's right," according to an interview with The Atlantic magazine on Sunday.

US Secretary of State Marco Rubio said Venezuela's next leader should be aligned with US interests. Those include keeping Venezuela's oil industry out of the hands of US adversaries and stopping drug trafficking.

He cited an ongoing US blockade on tankers under sanctions as leverage.

"That means their economy will not be able to move forward until the conditions that are in the national interest of the United States and the interest of the Venezuelan people are met," he said on ABC's "This Week."

The Venezuelan government has said for months Trump was seeking to take the country's vast natural resources, especially its oil, and officials made much of his comment on Saturday that major US oil companies would move in.

“We are outraged because in the end everything was revealed – it was revealed that they only want our oil,” added Cabello.

Some Maduro supporters gathered at a government-sponsored protest march on Sunday afternoon in Caracas.

Once ruled by Spain, Venezuela's "people must not surrender, nor should we ever become a colony of anyone again," said demonstrator Reinaldo Mijares.

"This country is not a country of the defeated.” (Reuters)