Venezuelan Interior Minister Nestor Luis Reverol said more arrests could follow in the incident, which he called a terrorist attack, according to the AP.
Venezuela's Minister of Communication says preliminary information shows the explosions came from several "drone-type flying devices" containing explosive charges that detonated in the vicinity of the presidential stage, . and in other areas of the parade.
Video footage from Saturday's political rally showed people running after what the Venezuelan authorities said was the detonation of two explosive drones.
One showed a cellphone video of a drone hovering over a residential street two blocks away and then crashing into a building.
The president later described the attack, which injured seven soldiers, as an assassination attempt.
Bolton said he spoke with the US government's top diplomatic official in Caracas, the Venezuelan capital, on August 5 and said that Americans in Venezuela are safe.
David Smilde, a senior fellow at the Washington Office on Latin America who has spent decades researching Venezuela, said the incident did not appear to be a staged attack by Maduro's government for political gain.
In this photo released by China's Xinhua News Agency, security personnel surround Venezuela's President Nicolas Maduro during an incident as he was giving a speech in Caracas, Venezuela, Saturday, Aug. 4, 2018.
"I have no doubt that everything points to the right, the Venezuelan ultra-right", Maduro said on Saturday night.
"These terrorist acts represent a slap in the face to the expressed desire of the President of the Republic, Nicolas Maduro, for national reconciliation and dialogue", Reverol said in a statement read on state television.
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He said they made improvements on security and the economy, saying the economic reforms are those in which "both of us will win". The moves drew howls from European capitals, and prompted of retaliatory tariffs on USA -made bourbon whiskey and motorcycles.
Police arrested the drone pilot, the witness said.
Within seconds, Maduro said he heard a second explosion and pandemonium broke out. "But in the meantime, I think what we really should focus on is the corruption and the oppression of the Maduro regime in Venezuela".
Another resident apparently saw the same drone.
Attorney General Tarek William Saab said the names of those arrested would be published on Monday. However, other accounts attributed the fire to the accidental explosion of a gas cylinder.
The Colombian foreign ministry denied involvement, saying the allegations were "absurd" and "lacked any foundation".
Speaking on "Fox News Sunday", Bolton said that if Venezuela had "hard information" of a potential violation of United States law, "we will take a serious look at it".
Maduro, a 55-year-old former bus driver, has effectively sidelined the fractured opposition through control of the courts and the electoral body - and unstinting support from the military, which holds key posts in his government. The government then announced on Sunday that six arrests had been made, with more on the way, and that it had identified "material and intellectual authors inside and outside the country".
Bolivian President Evo Morales, an ally of Maduro, took the accusations one step further and blamed the U.S., Pompeo and Vice President Mike Pence - calling it "Yankee Interventionism" - in a series of tweets Sunday afternoon.
Maduro often accuses the opposition and the United States of working together to foment a "coup" to topple him.