"A spokesperson for emperor Donald Trump said that they would not recognize the results of Venezuela's constituent assembly election", he told a rally of supporters shortly after Sunday's vote.
The US has said it is "deeply concerned" by the arrests. The two men each had posted videos urging their followers to boycott Sunday's election. He was released last month to serve the rest of his term under house arrest. He had been convicted of instigating violence during protests against Maduro in 2014 that left 43 people dead.
Maduro has drawn widespread global criticism over the election and for his threat to use the new assembly to punish his foes.
That would mean avoiding US mistakes such as the embarrassing absence of Secretary of State Rex Tillerson from the recent Organization of American States meeting of foreign ministers in Cancun, Mexico, to discuss the Venezuelan crisis. "What's just as bad: It would break the growing worldwide consensus we have today against Maduro's dictatorship".
Venezuela's defense minister, Gen. Vladimir Padrino Lopez, also appeared on television Tuesday to affirm his loyalty to Maduro. "I don't obey orders from foreign governments and never will". And it would make it much more hard to impose worldwide diplomatic sanctions against the Maduro regime.
Maduro has said the new constitution will bring peace while offering few details on how the document may be structured.
The poll rubber-stamped an assembly that would give Mr Maduro virtually unlimited powers - including the ability to change the constitution.
Furious government opponents are calling for four months of anti-government street demonstrations to be escalated. Both were reportedly sent to prison in Caracas.
Officials say more than 40 per cent of Venezuela's 20 million voters cast ballots Sunday.
His seat on the new body, confirmed by the electoral authority, will be his first foray into a higher-profile public role at age 27.
The constituent assembly itself has come under fire because it was created to rewrite the constitution and possibly supplant the opposition-led congress, whose members were elected in a conventional election in December 2015. Among other measures, he said he would use the assembly's powers to bar opposition candidates from running in gubernatorial elections in December unless they sit with his party to negotiate an end to hostilities that have generated four months of protests that have killed at least 120 and wounded almost 2,000. Venezuela sends cheap oil to USA energy firms, and oil sanctions would force the U.S.to buy oil elsewhere. Gasoline, medicine and such basic staples as cooking oil, flour, and sugar are scarce, and many Venezuelans cross into neighboring Colombia and Brazil to buy food.
Concerns about the impact of possible US sanctions on Venezuela helped lift oil prices above $50 a barrel on Monday for the first time in two months.
Panamanian and Argentine officials and the Organization of American States condemned Tuesday's arrests, though other nations in the region were silent.