Tensions have soared between the two nations after Trump recognized opposition leader Juan Guaido, who claimed Wednesday to hold the presidency and vowed to remove Maduro, calling him a "dictator".
But Secretary of State Mike Pompeo said in an interview Thursday that Maduro - to whom the military leadership is still loyal - bore responsibility for the safety of U.S. diplomats.
In a video addressing the military earlier this week, Guiado said the constitution requires them to disavow Maduro after his May 2018 re-election, which was widely condemned by the worldwide community because his main opponents were banned from running.
Bolton added that the process was "very complicated" and that officials were still studying how this would function. Guaido did not respond to a message seeking comment.
Venezuelan President Nicolas Maduro said on Thursday he will close the country's embassy and consulates in the United States, a day after severing "diplomatic and political" ties with Washington.
Guaido's bold move capped three days of high tension that began Monday when a group of soldiers took over a command post in the capital Caracas and rose up against Maduro.
But Guaido now leads what amounts to a shadow government disavowed by the armed forces and with no influence over day-to-day administration such as importing and distributing food and medicine.More news: Support for Trump's Border Wall Wanes Amid Government Shutdown Deadlock, Poll Shows
US Senator Marco Rubio is considered to have played a major role in convincing fellow Republican Trump to ratchet up pressure on Maduro, subtly reminding him of the importance of the Cuban-American vote in presidential swing state Florida.
His ascent was greeted with excitement by investors holding Venezuela and state oil company PDVSA bonds, which hit their highest level since 2017 despite being nearly entirely in default.
Russian Foreign Minister Sergei Lavrov, too, denounced USA policy on Venezuela as "destructive" while Russia is also backing Maduro.
Maduro has also shuttered USA missions in the United States.
Backing for him has come principally from the Western hemisphere.
Asked whether he was considering U.S. military intervention in Venezuela, Mr Trump told reporters: "We're not considering anything, but all options are on the table".
The European Union and United States ratcheted up the pressure on Maduro to agree to new elections, with an EU diplomat telling AFP the bloc wanted "an immediate call for elections in the near future".More news: Federer to play France's Roland Garros for the first time since 2015
Maduro, in a rambling speech, dismissed Guaido's inauguration and said he himself remained the country's legitimate leader. Inflation is forecast to hit 10 million percent this year.
Guaido has said Maduro's January 10 inauguration to a second six-year term amounted to a usurpation of power.
But others remain steadfast in their backing of Maduro, with both Turkey and Russian Federation confirming their on-going support.
In an interview with broadcaster Univision on Thursday, Guaido described the recent events as "the beginning of the end" for Maduro, who has presided over Venezuela's worst ever economic crisis.
"Can he name ministers?"
Another young comrade patrolling a busy road leading to the Supreme Court with the teen said he hadn't seen the video images of military leaders proclaiming their support to Maduro because he doesn't own a cellphone but that he follows orders as instructed. "Is he going to name commanders of military units?"
But there were no signs that security forces were widely heeding Guaido's call to go easy on demonstrators. Dozens of protesters have been killed in the unrest.More news: Ariana Grande Targeted for Potential Plagiarism