And a loyalist super-legislature Maduro created last year, the Constituent Assembly, was debating a measure to strip opposition lawmakers of their parliamentary immunity to face trial over Saturday's drone incident.
Venezuelan authorities have already arrested one lawmaker, 29-year-old Juan Requesens, and were preparing to put him on trial.
Intelligence officers "came to his home and forcibly took him away without any warrant" late Tuesday, his father Guillermo Requesens told reporters.
Maduro has blamed Borges, the former head of the opposition-dominated National Assembly, and Requesens of involvement in the drone "attack."
On Saturday, Maduro halted his speech at a Caracas military parade because of a detonation he said was caused by a drone carrying explosives, and dozens of soldiers ran away in panic.
The embattled president said neighboring Colombia was behind the "assassination" plot in collaboration with Venezuela's opposition.
He is pressing Colombia and the United States to extradite figures he sees as plotting against him.
Borges, who on Tuesday attended the swearing-in of Colombia's new president, Ivan Duque, called Maduro's accusation against him "a farce."
"Everyone knows that it's a set-up to persecute and convict anybody that opposes your dictatorship," Borges wrote on Twitter.
Intensifying 'repression'
Venezuela's attorney general, Tarek William Saab, said Wednesday that three of seven suspects arrested in the wake of the incident had appeared before a judge.
He said Requesens would go on trial once he was stripped of his immunity.
The National Assembly however has said it will dismiss any attempt to remove its members' immunity as unconstitutional.
Venezuela's opposition has been systematically sidelined by Maduro, who has used his control of the Supreme Court, electoral authorities and security forces to concentrate power in his hands.
The Eurasia Group, a risk consultancy, said that following the drone attack, "the immediate impact will be for Maduro to intensify repression against his opponents and close ranks."
It added that, while there was no imminent fall predicted for Maduro, "holding onto power will become increasingly challenging in the long term, particularly if he fails to provide guarantees and privileges to key stakeholders amid deteriorating economic conditions, and while social dynamics remain fragile."
After establishing the rival, all-powerful Constituent Assembly last year, four months of violent protests and repression flared, killing 125 people.
Venezuela's diplomatic isolation also deepened, with most countries in the Americas slamming Maduro as undemocratic and increasingly dictatorial.
The political turmoil has worsened Venezuela's ability to respond to its economic collapse.
The country, once one of the wealthiest in Latin America, is on the brink of total default as exports of oil -- the resource it depends upon -- decline and with them the hard currency Maduro's government needs.
Venezuela is in the grip of staggering hyperinflation, shortages of food and medicine, and is seeing an exodus of hundreds of thousands of its citizens, creating a regional humanitarian emergency.