Venezuelan politician Delcy Rodríguez has taken over the helm of the South American country after the United States siezed leader Nicolás Maduro - and she has already been given a stern warning by President Donald Trump.

Venezuela's presidential website uploaded images and statements late on Sunday, January 4, of the long-time vice-president chairing an emergency meeting of the Council of Ministers in the capital Caracas.

Officials confirmed the gathering was the first cabinet meeting under Rodríguez's leadership. A statment said it was her first meeting as the acting president of the Bolivarian Republic of Venezuela.

Maduro, 63, and his wife Cilla Flores, 69, were captured by an elite squadron of the US military in an overnight raid on Saturday, January 3. The Venezuelan leader of 12 years has been called a dictator and indicted on drug and terrorism charges at a court in the Southern District of New York in 2020.

His wife and four others may be charged by the US with narco-terrorism conspiracy and other charges, according to documents posted online by US Attorney General Pam Bondi on Saturday morning after the couple's capture.

On top of the narco-terrorism conspiracy charge, the indictment alleges four other criminal counts: cocaine importation conspiracy, possession of machine guns and destructive devices and conspiracy to possess machine guns and destructive devices.

Rodríguez said in an statement that she hopes to build "respectful relations" with Trump and his country. She invited the US government "to collaborate with us on an agenda of cooperation oriented towards shared development within the framework of international law to strengthen lasting community coexistence".

In the same press statement, Rodríguez branded Maduro's removal a "temporary absence" before accusing the US of "kidnapping" the ousted president and his wife. She called the incident an illegal act of aggression.

State TV has not shown a formal swearing-in ceremony and Rodríguez stopped short of openly declaring herself interim leader during a televised address on Sunday.

A scrolling ticker beneath her speech still labelled her as vice-president and she did not mention a political transition or change to top leadership.

Rodríguez also appeared to reject Trump's claim that she would cooperate with the US.

"What is being done to Venezuela is an atrocity that violates international law... history and justice will make the extremists who promoted this armed aggression pay," she said in the address.

Trump on Sunday warned that if Rodríguez does not cooperate that "she is going to pay a very big price, probably bigger than Maduro".

His comments come after US States Secretary of State Marco Rubio said during his own TV interviews on Sunday that he does not deem Rodríguez or her government as "legitimate" since Venezuela does not hold free and fair elections, the Associated Press reported.