Delcy Rodríguez was sworn in as Venezuela's interim president in a parliamentary session that began with demands for the release of ousted leader Nicolás Maduro from US custody.

Rodríguez, 56, vice president since 2018, said she was pained by what she called the "kidnapping" of Maduro and his wife, Cilia Flores, who were seized by US forces in an overnight raid on Saturday.

In a dramatic scene inside a New York court room two hours earlier, Maduro had insisted he was still president of Venezuela as he pleaded not guilty to four charges of drug trafficking and terrorism.

Meanwhile the US faced sharp criticism at the UN, but the US ambassador responded that the largest energy reserves in the world could not be left in the hands of an illegitimate leader, a "fugitive from justice".

Before the court appearance, the UN Security Council held an emergency session to discuss the situation in Venezuela.

The ambassador for Venezuela, Samuel Moncada, said his country had been the target of an "illegitimate armed attack lacking any legal justification".

The US ambassador to the UN, Mike Waltz, justified the attack by describing Maduro as "an illegitimate so-called president".

Waltz added that the US had carried out a "surgical law enforcement operation" to apprehend Maduro, whom he also referred to as a "fugitive from justice".

Maduro has been accused of narco-terrorism conspiracy, cocaine importation conspiracy, possession of machine guns and destructive devices and conspiracy to possess machine guns and destructive devices.

During Monday afternoon's court appearance, a member of the public began to yell in Spanish at Maduro that he would "pay" for what he had done.

Maduro turned to him and replied that he was a "kidnapped president" and a "prisoner of war" before being escorted out in shackles behind his wife through the back court door.

"I'm a decent man. I am still president of my country," Maduro said earlier during the 30-minute hearing.

Judge Alvin Hellerstein, 92, interjected to tell Maduro that there would be a "time and a place to get into all of this".

Speaking just hours after Saturday's attack - which saw over 150 aircraft and 200 US personnel enter Venezuela - Trump vowed the US would "run" Venezuela until "a safe and proper and judicious transition" was possible.

Later on Monday, following a two-and-a half-hour classified briefing at the US Capitol, US Senate Minority Leader Chuck Schumer said the US plan for running Venezuela was "vague, based on wishful thinking, and was unsatisfying".

"I did not receive any assurances that we would not try to do the same thing in other countries," he said.

"When the United States engages in this kind of regime change and so-called nation building, it always ends up hurting the United States."

US Speaker of the House Mike Johnson denied the US was carrying out regime change, saying it was "a demand for a change of behaviour by a regime".

Describing the operation as "decisive and justified", he said the US had "always maintained the right to use force to defend our national interest, to preserve the safety of the American people and to prevent ongoing threats to its security".

"We have a way of persuasion," Johnson said, "because their oil exports, as you know, have been seized, and I think that will bring the country to a new governance in very short order."

Trump has also promised US oil companies would move into the country to fix infrastructure "and start making money for the country".

But despite the US president's claims, Maduro's allies remain in charge.

In comments made to the US magazine The Atlantic on Sunday once it became clear Rodríguez would be sworn in, Trump warned she could "pay a very big price, probably bigger than Maduro" if she "doesn't do what's right".

During a cabinet meeting, Rodríguez indicated her government would engage in some cooperation with the US, saying: "We invite the US government to collaborate with us on an agenda of co-operation orientated towards shared development within the framework of international law."

Thousands of Venezuelans gathered outside the Federal Legislative Palace to show support for Maduro, his wife and the interim president Rodríguez as she was sworn in.

Speaking after taking her oath, Rodríguez told the National Assembly she did so "with pain" because of the suffering caused by "illegitimate military aggression".

She vowed to guarantee the peace of the country, "the spiritual tranquillity of our people, the economic and social tranquillity of our people".

The assembly also heard from Maduro's son who expressed his support for his parents - saying that they "will return" to Venezuela.

He also offered his "unconditional support" to Rodríguez.

The next court hearing in Maduro's case has been scheduled for 17 March. (BBC)

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