Four grenades were hurled at the high court from a helicopter and bullets were fired at the interior ministry yesterday, Maduro said, in a potentially dramatic escalation of the violence gripping the oil-rich South American country.
The attack was claimed in a video released online by a man identified by media and the government as 36-year-old Oscar Perez.
Beyond his police work, Perez has acted in a Venezuelan action film, "Suspended Death," and has posted photographs on social media of himself posing with weapons.
Maduro has for months been fending off calls for elections to replace him, from opponents who blame him for a desperate economic crisis that has sparked hunger and deadly violence.
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He so far retains the public backing of the military high command -- a factor that analysts say is decisive if he is to remain in power.
Venezuela has seen three attempted military coups since 1992.
The government named Perez as the author of the attack, saying he had stolen a police helicopter.
He branded the attack part of an "escalation" by right- wing "coup" plotters.
"I have activated the entire armed forces to defend the peace," he said in remarks broadcast from the Miraflores presidential palace.
"Sooner or later, we are going to capture that helicopter and those that carried out this terrorist attack."
Photos circulating on social media showed a helicopter flying over Caracas as explosions were heard.
In the video published by Venezuelan media, Perez called on Maduro to resign and for early elections to be held.
Maduro called on the opposition MUD alliance to denounce the attack, but its leaders said there was not yet enough information to comment.
"Whatever it is, it is very serious. It all points to one conclusion: that the situation in Venezuela is unsustainable."
Borges said pro-government military officers had scuffled with opposition lawmakers in congress yesterday and blocked them in the chamber for several hours.
Another senior opposition lawmaker, Freddy Guevara, urged people to take part in anti-government rallies today -- the latest in nearly three months of daily streets protests that have left 76 people dead.
Earlier yesterday, Maduro warned US President Donald Trump that Venezuela would fight back against such a move.
"If Venezuela were dragged into chaos and violence... We would fight," Maduro bellowed in a speech to supporters.
If a coup prevented his side from fulfilling his contested reform plans, he said, "we would achieve it by arms."
"I am not exaggerating when I say it would have involved the arrival of American ships and troops in Venezuelan waters, on Venezuelan soil," Maduro said.
The international community has called for mediation to solve the crisis after Vatican-backed talks last year broke down.
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