The group, which describes itself as uniting members of "the resistance" to Maduro, said it had planned to fly two drones but that snipers shot them down.
The assailants flew two drones each packed with two pounds of C-4 plastic explosive toward Maduro, his wife, and other top leaders as he spoke at an event celebrating the 81st anniversary of the National Guard, the AP quoted Reverol as saying.
New footage has emerged showing the moment a drone bomb exploded over Venezuelan President Nicolas Maduro while he gave a speech to a crowded event in Caracas on Saturday in what he claims to be an attempt on his life.
Colombia also rejected Maduro's "absurd" accusation of involvement.
Attorney-general Tarek William Saab said some "material authors" of the apparent attack had been detained and prosecutors had already obtained critical details with further details to be given today. It came from the sky and we thought it was a boy playing with it, " said Pedro Peña, 62, who was in a seventh floor apartment with Gladys Miquelena, 56.
"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.
Maduro said investigations pointed to financial backers who "live in the United States, in the state of Florida".
Trump's adviser, John Bolton, says he can state "unequivocally" that "there was no USA government involvement in this at all". "I hope that President Donald Trump is ready to fight these terrorist groups".More news: 'Stand your ground' law protects gunman in deadly shooting over parking spot
"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 nor teaches, only indoctrinating communism", said the statement, accusing the regime of having "made public office an obscene way to get rich".
The head of the assembly, Diosdado Cabello, tweeted that Maduro and the assembled military chiefs had survived a "terrorist attack" he blamed on the opposition.
Apparently in response, Bolton said, "If the government of Venezuela has hard information that they want to present to us that would show a potential violation of USA criminal law, we'll take a serious look at it". Hundreds of thousands of Venezuelans have left the country over this time, and previous year, 125 people were killed across four months of clashes between Venezuelan authorities and anti-regime protesters.
Seen as authoritarian and repressive by his detractors, Maduro has relied heavily on the military to hold on power in the face of a crippling economic crisis and political turmoil.
Hundreds of thousands have fled the country due to food and medicine shortages and hyperinflation that the International Monetary Fund says could reach one million percent this year.
Later Mr Maduro said the incident had strengthened his resolve.
Both Cuban leaders expressed their "full solidarity and unconditional support for President Maduro", it said.
Maduro this year brought forward to May presidential elections that - after they were boycotted by the opposition and key opposition figures were declared ineligible - handed him a new six-year term.