While the United States has been ratcheting up sanctions on Venezuelan officials, it has to tread lightly to avoid accusations from the region of meddling, said David Smilde, a senior fellow with the Washington Office on Latin America.
Venezuela is in economic turmoil which the opposition says has been worsened by Mr Maduro, whom they accuse of wanting to create a dictatorship.
State media largely ignored Sunday's event, concentrating instead on a simultaneous, government-organised practice run for the July 30 vote.
Sunday's participation by almost 7.2 million Venezuelan voters, compared with 7.7 million opposition votes in the 2015 legislative elections, which they won by a landslide, and the 7.3 million votes for the opposition in a 2013 presidential poll narrowly won by Maduro.
Venezuela's Opposition called a nationwide strike for Thursday to press President Nicolas Maduro to abandon plans of rewriting the constitution, ratcheting up tensions after an unofficial vote rejecting Maduro's plan, and amid months of deadly protests.
In response to another question, voters urged the military to defend the current constitution.
"We have received a clear mandate of 7.1 million to be sure that we will achieve a democratic change. The vote by millions of Venezuelans was an unequivocal affirmation in support of free and fair elections as well as respect for the existing constitution", she said. The court is controlled by loyalists of Maduro's ruling socialist party.
The Opposition set the scene for the strike with its vote Sunday, which it called a "plebiscite" but which the Government dismissed as "illegal". He says he stays informed about what is going on his native country from his parents, though the majority of his family remains in Venezuela. They said it's all to stand up to the Venezuelan government.
Protesters are demanding a new presidential election and want Maduro to lift his ban on humanitarian aid so that needed food and medical supplies can reach Venezuelans.
Which is why, over the weekend, Maduro confidently huddled with cabinet ministers and leaders of his socialist party and assured them the constituyente will begin as planned on July 30 with the election of a special constitutional assembly. Still, some supporters said they were disappointed.
Maduro claimed that the simulation of the ANC vote as having seen "very big" participation, larger than any election for 18 years.
"If he doesn't, there not only will be more violence, but it will cause the fall of his government", Borges said in an interview.
Also on Sunday, Maduro reiterated his call for political dialogue with the opposition.
Any stepped-up confrontation between the opposition and the government threatened to deepen a political crisis that, since the beginning of April, has left 100 people dead.