The government said seven soldiers were wounded in the alleged attack Saturday, blamed on Colombia by Maduro and later claimed by a mysterious rebel group.
"I am fine, I am alive, and after this attack I'm more determined than ever to follow the path of the revolution," Maduro said defiantly of the incident, from which he escaped unharmed.
"Justice! Maximum punishment! And there will be no forgiveness," he warned in an address to the nation.
Meanwhile, Attorney General Tarek William Saab, also present at the parade, said those arrested in connection with the incident would be identified on Monday.
Venezuelan state television images showed Maduro looking up disconcertedly in the middle of a speech having heard a bang, before members of the country's National Guard lined up in the parade suddenly scattered.
"It was an attack to kill me, they tried to assassinate me today," he said in a state broadcast, speaking of a "flying object (that) exploded in front of me."
Communication Minister Jorge Rodriguez said there was "an explosive charge... detonated close to the presidential podium" and in several other spots along the parade held in central Caracas. Saab told CNN he saw a drone filming the event explode.
No drones could be seen in the television broadcast, which showed bodyguards jumping in front of Maduro to protect him with flexible ballistic shields. The broadcast was quickly cut.
Meanwhile, a policeman who requested anonymity told AFP that drones may have been released from a nearby apartment that suffered a fire after one exploded. However, other versions of events attributed the fire to the accidental explosion of a gas cylinder.
The government pointed the blame at "the ultra-right wing" - its term for the opposition.
But Maduro himself said: "I have no doubt that the name (outgoing Colombian President) Juan Manuel Santos is behind this attack."
He added investigations pointed to financial backers who "live in the United States, in the state of Florida. I hope that US President Donald Trump is ready to fight these terrorist groups."
The Colombian foreign ministry denied involvement, saying the allegations were "absurd" and "lacked any foundations."
A senior US State Department official said the White House was monitoring the situation closely, without commenting further.
Elsewhere, Maduro's allies Cuba and Bolivia condemned the incident.
In a statement, the Russia foreign ministry said: "We strongly condemn the assassination attempt on the President of the Bolivarian Republic of Venezuela."
Late Saturday, a civilian and military rebel group calling itself the "National Movement of Soldiers in T-shirts" claimed responsibility.