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 leftist leader 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.

As Monday's session opened, lawmakers chanted: "Let's go Nico!" -- a slogan of Maduro's presidential campaign ahead of 2024 elections that were widely denounced by the opposition and dozens of global capitals, including Washington, as fraudulent.

On President Donald Trump's orders, US military forces early 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.

Witnesses said shots were fired late Monday near the presidential palace, with a source close to the government saying the situation was under control.

Unidentified drones flew over the Miraflores palace in central Caracas and security forces opened fire in response around 8:00 p.m., the source said, hours after Rodriguez was sworn in.

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 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."

New members of Venezuela's single-chamber parliament were chosen last May in elections boycotted by much of the opposition, leaving 256 of the 286 seats in the hands of the ruling United Socialist Party of Venezuela (PSUV) and its allies.

Maduro Guerra said Monday 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.

Delcy Rodriguez, who on Saturday insisted Maduro remains the country's "only" president, later extended an offer of cooperation to Washington, who has said it would work with Venezuela's leaders if they do what it wants.

Trump meanwhile warned Rodriguez could face a fate worse than Maduro if she failed to heed US demands on policy reforms and oil access.

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