New York, New York - Venezuelan President Nicolás Maduro pleaded not guilty to charges of "narco-terrorism" in a New York court on Monday, two days after being abducted in a violent coup staged by US forces.

Maduro reportedly told a federal judge in Manhattan that he had been kidnapped from Venezuela and said "I'm innocent, I'm not guilty."

"I'm still the president of my country," he was quoted as saying.

Media footage from Monday showed him being escorted earlier by DEA agents and wishing reporters a "happy New Year."

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Maduro's wife Cilia Flores likewise pleaded not guilty.

The pair were abducted by US commandos in the early hours of Saturday in an assault backed by warplanes and a heavy naval deployment – a stunning violation of international law, according to experts.

In a series of shock announcements over the weekend, President Donald Trump declared that the US is now running Venezuela with a view to rebuilding and controlling its huge oil industry.

Amid international alarm, UN Secretary-General António Guterres told an emergency Security Council meeting that there should be "respect for the principles of sovereignty, political independence and territorial integrity."

There was sharp criticism Monday from Mexico, where President Claudia Sheinbaum said the Americas "do not belong" to anyone.

Colombian President Gustavo Petro issued a fiery statement saying that as a former guerrilla fighter he was ready to "take up arms" against Trump, who had threatened to oust him as well.

Maduro became president in 2013, taking over from his socialist predecessor Hugo Chavez. The US and European Union claim he stayed in power by rigging elections and imprisoning opponents, while overseeing rampant corruption.

Accusations that he is personally involved in drug-trafficking have not been backed up with evidence.

Some 2,000 Maduro supporters, including rifle-wielding men on motorcycles, rallied Sunday in Caracas, waving Venezuelan flags.

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On Monday, deputies in the Venezuelan parliament shouted "Let's go, Nico!" in support for the ousted leader, while protesters also showed up outside the courthouse in Manhattan to demand his release.

For now, the Trump administration has indicated it wants continuity with the remainder of Maduro's administration – provided they submit to US rule.

Interim president Delcy Rodriguez, who was Maduro's vice president, dropped an initially defiant posture on Sunday, later saying she was ready for "cooperation" after more explicit threats of aggression from Trump.