"I have no doubt that everything points to the right, the Venezuelan ultra-right", Maduro said on Saturday night.
Both Cuban leaders expressed their "full solidarity and unconditional support for President Maduro", it said.
He said one of the drones flew over the tribune where Maduro was giving a speech to mark a military parade but that it became "disoriented by signal inhibiting equipment" and was thus "activated outside the assassins' planned perimeter".
One of the witnesses - who showed the AP cellphone video of a drone hovering over a residential street two blocks away and then crashing into a building - said the police arrested the machine's pilot.
Mr Maduro, 55, a deeply unpopular leader who was re-elected after a disputed vote in May, said the "far right" working with detractors in Bogota and Miami, including Colombian president Juan Manuel Santos, were responsible.
The people on stage looked up, startled as the explosion was heard.
Photos on social media show bodyguards lifting multiple bulletproof shields in front of Maduro.
Maduro, who blames the country's problems on an "economic war" led by adversaries, during the course of his five-year rule has often announced having foiled military plots against him that he says are backed by Washington.
"It's evident that the initial reaction of the government isn't aimed at attempting to clarify what happened but rather to take advantage of the situation and irresponsibly and sweepingly attack the 'opposition,"' the group said in a statement. The broadcast was quickly cut.
US President Donald Trump has been harshly critical of Maduro's leftist regime, saying it has "destroyed a prosperous nation by imposing a failed ideology".
A little-known group called the "National Movement of Soldiers in T-shirts" claimed responsibility for the attack.
USA national security advisor John Bolton insisted Sunday that there was "no U.S. government involvement" and even suggested on "Fox News Sunday" that the incident could have been "a pretext set up by the regime itself".
"If the goal of a government is to achieve the greatest amount of happiness possible, we can not tolerate that the population is suffering from hunger, that the sick do not have medicine, that the currency has no value, or that the education system neither educates or teaches, only indoctrinating communism", added the statement.
He said the second drone lost control and fell into an apartment building, where it exploded on the first floor. However, other accounts blamed the fire on the accidental explosion of a gas cylinder.
Opposition critics accuse Maduro of fabricating or exaggerating security incidents to distract from hyperinflation and Soviet-style product shortages.
Maduro has remained in power over Venezuela, a major oil exporting nation, despite a collapsing economy and a long-running political crisis that has seen his country isolated internationally.
Last year, 125 people were killed over four months of violent clashes between anti-Maduro protesters and armed forces.