The government alleged that opposition factions conspired with assailants in Miami and Bogota, although they offered no specific evidence.
Venezuela, a once-wealthy oil-producing nation, is in the midst of a five-year crisis under Maduro's socialist government.
The attack against President Maduro took place at the 81st anniversary of the Bolivarian National Guard, in which two drones carrying explosives were detonated near the presidential platform, injuring seven military personnel and halting Maduro mid-speech.
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".
"We consider using terrorist methods as a tool for political struggles to be categorically unacceptable", the statement said, adding "it is obvious that such actions are aimed at destabilising the situation in the country following the congress of the Socialist Party of Venezuela, which outlined priority steps to restore the economy". "In the next hours there could be more arrests".
Moscow sided with Maduro's regime after his government faced worldwide isolation when close to 130 people were killed in anti-regime protests previous year. One took part in 2014 protests that rocked the nation as it descended into an economic crisis that is now worse than the Great Depression.
The foreign minister of Venezuela Jorge Arreaza said Sunday that the attack against President Nicolas Maduro a day earlier was a manifestation of frustration against the president and against those in positions of state.
Authorities found various nearby buildings that were struck by the explosions.
The other machine collided into a nearby building and exploded, he said.
One showed a cellphone video of a drone hovering over a residential street two blocks away and then crashing into a building.
Another witness, Mairum Gonzalez, described running in panic to her fifth-floor balcony, where she heard the second explosion and saw smoke rising.
Cuban President Miguel Diaz-Canel and his predecessor Raul Castro "strongly condemn the attempted attack against President Nicolas Maduro", the Cuban foreign ministry said on its Twitter account. He at first thought it might be a pyrotechnics display.
Reverol said one of the detained had an outstanding arrest warrant for his alleged role in the August 2017 attack on a military base in Valencia. Bodyguards escorted him from the event, covering him in black shields, and TV footage showed uniformed soldiers break formation and scatter.
"It was an attack to kill me, they tried to assassinate me today", Maduro said in a later state broadcast, speaking of a "flying object (that) exploded in front of me".
"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.
The United States on Sunday denied any involvement in the alleged "assassination" attempt.