Backed by hundreds of thousands of protesters and the support of the United States, Mr Guaido has declared himself interim president and called for free elections to end the rule of Mr Maduro.
Venezuelan opposition leader Juan Guaido declared he was temporarily assuming presidential powers in a bid to unseat Nicolas Maduro.
Russian Federation opposes the request and has accused Washington of backing a coup attempt, placing Venezuela at the heart of a growing geopolitical duel.
The battle between Mr Maduro and Juan Guaido sets up a potentially explosive struggle for power in the crisis-plagued South American nation.
FILE - Canadian Foreign Minister Chrystia Freeland takes part in a news conference at the Embassy of Canada in Washington, U.S., August 31, 2018.
A video circulating on social media showed the same caravan leaving the embassy, a fortified compound overlooking the center of the Venezuelan capital.
The diplomats were likely to leave Caracas around midday on one of two daily flights to Miami by American Airlines, the last-remaining USA carrier to serve Venezuela after Delta and United Airlines pulled out in 2017 amid a political crisis that has forced millions to flee the country.
It did not immediately respond to a request for comment on the movement of embassy personnel on Friday.
That was the conclusion drawn from United States contacts with Guaido in the days ahead of his declaration, including two phone calls with Pence, officials said, asking to remain anonymous because of the sensitivity of the situation.
However, he still has no control over the Venezuelan state and the military, which appears to still be loyal to Maduro despite a deep economic and political crisis.
Diplomats at the Organization of American States held an emergency meeting Thursday on the Venezuelan crisis, during which 16 nations recognized Guaido as interim president. Mexican President Andres Manuel Lopez Obrador said on Friday his administration would be willing to mediate.
Maduro has also called home all Venezuelan diplomats from the US and closed its embassy in Washington Thursday.
Guaido is also readying a new board to run state-run oil firm PDVSA's US unit Citgo Petroleum, people familiar with the discussions said.
One senior official, who spoke on condition of anonymity, said there was concern among some in the department that by recognizing Guaido the United States would divide the region, especially as Mexico's new leftist government supports Maduro.
Describing hard-left President Maduro as "illegitimate", US President Donald Trump said on Thursday the National Assembly, headed by Guaido, is "the only legitimate branch of government duly elected by the Venezuelan people".
In a video earlier this week, Guaido said the constitution requires the military to disavow Maduro after his May 2018 re-election, which was widely condemned by the global community because his main opponents were banned from running.
"Venezuela is friendly to us and is our strategic partner".
However, Trump has taken an increasingly tough line with Venezuela since he took office in January 2017, imposing an escalating series of targeted sanctions.
A senior United States official, speaking on condition of anonymity, warned Mr Maduro and his loyalists that Washington was ready to ramp up oil, gold and other sanctions.
"We know that this will have consequences", Guaido shouted to the cheering crowd before slipping away to an unknown location amid speculation that he would soon be arrested.