Venezuela's parliament swore in Delcy Rodriguez as interim president on Monday, two days after US forces seized her predecessor Nicolas Maduro to face trial in New York.

Rodriguez, who has indicated she will cooperate with Washington, took the oath of office during a ceremony in the National Assembly, telling lawmakers she was doing so "in the name of all Venezuelans."

She said she was "in pain over the kidnapping of our heroes, the hostages in the United States," referring to Maduro and his wife Cilia Flores, who face drugs charges in New York with other Venezuelan officials.

Parliament denounced the capture of Maduro while vowing support for his stand-in Rodriguez after the US military attack that shocked Caracas and the world.

Outside the legislature, thousands of Venezuelans gathered to demand the release of their leader, chanting: "Maduro, hold on: Venezuela is rising!"

"Regardless of whether Nicolas Maduro has something to answer for in court, this was not the way to do it," protestor Flur Alberto, 32, told AFP.

Inside, meanwhile, members of the National Assembly offered their full backing to Rodriguez – who had been Maduro's vice president – and reelected her brother Jorge Rodriguez as parliament speaker.

On President Donald Trump's orders, US military forces on Saturday launched strikes on the Venezuelan capital and seized Maduro and his wife, flying them to New York to stand trial on drug trafficking charges.

"The president of the United States, Mr Trump, claims to be the prosecutor, the judge, and the policeman of the world," senior lawmaker Fernando Soto Rojas said in an address to colleagues.

"We say: you will not succeed. And we will ultimately deploy all our solidarity so that our legitimate president, Nicolas Maduro, returns victorious to Miraflores," the presidential palace, he added.

Venezuela's Supreme Court on Saturday ordered Delcy Rodriguez to assume the presidency "in an acting capacity," and on Sunday the military also threw its support behind her.

With Jorge Rodriguez's reelection, the influential siblings are in control of Venezuela's executive and legislative branches.

Jorge Rodriguez vowed in front of his lawmaker colleagues on Monday to pursue "all procedures, all platforms, and all avenues to bring back Nicolas Maduro Moros, my brother, my president."

Maduro's lawmaker son Nicolas Maduro Guerra also offered his support for the acting president.

"Count on me, count on my family," Maduro Guerra, known as "Nicolasito," told Rodriguez during an address to parliament, adding the country was "in good hands" until his parents' "return."

He added that Venezuela "asks for neither privileges nor concessions; it demands respect... We want international relations with everyone, based on equality, mutual respect, and cooperation, without threats and without interference."

He stepped outside to address the protesters, telling them he was in "indirect" contact with his father.

"We have a strong team over there that's supporting us," he said. (AFP)