Both have been charged by the Justice Department with narco-terrorism and other offenses.
"I am innocent. I am not guilty of anything that is written here," Maduro said in court as the charges against him were read.
In Maduro's absence, Delcy Rodríguez, his former number two, has been sworn in as the interim president of Venezuela. Rodriguez, 56, has long been a confidant and backer of Maduro.
She was the country's vice president from 2018 through Sunday.
Despite denouncing the U.S. military operation, Rodriguez said in a Sunday social media post that the country aspires towards balanced and respectful international relations between Caracas and Washington.
"We invite 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," she wrote.