US Secretary of State Mike Pompeo had claimed Tuesday that Maduro was on the cusp of fleeing to Cuba before being talked into staying by Moscow.
"The (FAA) order comes on a day of an information battle waged between Maduro and Guaido, and although the coup status is uncertain, one thing is clear: taking your aircraft to Venezuela is not a good idea", OPSGROUP said on its website.
"The national armed forces have taken the correct decision, and they are counting on the support of the Venezuelan people", Guaido said.
Bolton named Venezuelan Defense Minister Vladimir Padrino, Supreme Court chief judge Maikel Moreno and presidential guard commander Ivan Rafael Hernandez Dala as having told the opposition that Maduro needed to give up power to opposition leader Juan Guaido.
The video appeared to have been recorded at dawn in or near La Carlota air force base in Caracas.
The streets of Caracas, Venezuela have turned into chaos Tuesday after a military vehicle drove directly into a crowd of protesters.
The US White House led support for Venezuelan self-declared President Juan Guaido's push for a military uprising against interim President Nicolas Maduro on Tuesday, while Maduro's worldwide backers condemned the push as a coup.
The Trump administration has blamed Cuba and Russian Federation for Guaido's failure to wrest control of Venezuela from Maduro, and after Tuesday's failed coup attempt, Trump threatened to punish Cuba with further sanctions and an embargo, even though Cuba has been subject to a near-total U.S. embargo since 1962. Earlier this year, the United States banned the sale of Venezuela's oil in USA markets, adding more financial pressure on the country.
Tens of thousands of people reportedly marched in Caracas in support of Guaido early on Tuesday, clashing with Maduro's supporters and riot police.
Of the Cubans, Pompeo said "it is unacceptable that they are protecting this thug". "They are very actively collaborating", said Mark Weisbrot, who is co-director of the Center for Economic and Policy Research in Washington and has called for a negotiated end to the political crisis.
Former Vice President Joe Biden backed Venezuelan Interim President Juan Guaidó on Tuesday afternoon, who is fighting to gain control of the country.
Who is Venezuela's legitimate leader?
"We don't see any indication that there's any substantial part of the military that's ready to fire on innocent civilians, their fellow countrymen", added Bolton.
In the televised address, Maduro also made public the appointment of Gustavo Gonzalez Lopez as the head of the Sebin intelligence agency.
As he and the president have emphasized repeatedly for months, Bolton said all options remain on the table when asked about the possibility of US military intervention.
Meanwhile, Spain's socialist caretaker government urged restraint, while the governments of Cuba and Bolivia reiterated their support for Maduro.
Although Trump has repeatedly said "all options" are on the table regarding Venezuela - including, implicitly, military action - there has been no noticeable United States military mobilization.
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