Interior Minister Reverol said six "terrorists and hired killers" had been arrested, several vehicles seized and hotels raided.
Reverol says the second drone crashed into a nearby building and exploded.
One witness showed The Associated Press cellphone video of a drone crashing into a building.
Reverol said the 2 pounds of explosives on each drone could have affected an area of more than 160 feet. Seven NationalGuard soldiers were injured, Rodriguez added.
U.S. national security advisor John Bolton insisted there was "no USA government involvement" and even suggested that the incident could have been "a pretext set up by the regime itself".
Watch an alleged drone attack on Venezuela’s president sends soldiers fleeing
Venezuelan opposition leaders are fearing a crackdown and increased repression following a freakish, alleged assassination attempt against the country's strongman president, Nicolas Maduro on Saturday night in Caracas.
"And I have no doubt that everything points to the right-to the Venezuelan ultra-right, in alliance with the Colombian far-right", he said, adding that "Colombian President Juan Manuel Santos is behind this attack", according to a translated comment reported by El Nacional.
"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.
He said it was "a crime of terrorism and assassination" and that the "material and intellectual authors inside and outside the country" had been identified, with further arrests "in the coming hours" possible. "Seconds later there was a second explosion".
Officials say attackers flew drones loaded with explosives toward the president during an open-air military ceremony that was broadcast on live television.
Another resident apparently saw the same drone.
The Colombian government was quick to deny any involvement, saying there was "no basis" to Mr Maduro's allegations.
While Maduro was speaking about Venezuela´s economy, the audio suddenly went and he and others on the podium looked up, startled. Bodyguards surrounded Mr Maduro, 56, holding up bulletproof shields as he was led from the stage.
A year ago, four months of street protests flared against his authority that were put down by robust action from the army, the National Guard and police, resulting in 125 people killed.
An earlier account by firefighters at the scene of the blast hand linked the explosion to a gas leak.
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".
Venezuela has already reacted to Saturday's events with a series of arrests as Attorney General Tarek William Saab, who was also present at the parade, warning: "There will be a ruthless punishment".
Venezuela's government routinely accuses opposition activists of plotting to attack and overthrow Maduro.
Maduro, a 55-year-old Socialist leader who took over from his late mentor Hugo Chavez in 2013, has effectively sidelined the fractured opposition through control of the courts and the electoral body - and undinting support from the military, which holds key posts in his government.