Maduro has called for the creation of a "constituent assembly", a Soviet-like body that will seek to modify the country's constitution.
The opposition believes changing the constitution will only empower Maduro, though.
"Yet their strong and courageous actions continue to be ignored by a bad leader who dreams of becoming a dictator", he continued.
In Venezuela and in expat communities around the world, opposition organizers say 7.6 million Venezuelans sent a message to socialist President Nicolás Maduro: Do NOT rewrite Venezuela's constitution.
Trump did not specify what measures could be taken.
"The state of the foreign reserves and the general waste of Venezuela's foreign exchange earnings is one of the saddest stories of modern economic history", Universidad Central de Venezuela economist Javier Hernández told AFP.
Trump's stance explicitly sided with Venezuela's opposition, which accuses Maduro of trying to accumulate dictatorial powers to hang on to the reins.
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.
There was no immediate reaction from the Venezuelan president.
On Monday, Colombian President Juan Manuel Santos was in Havana meeting with Cuban leader Raúl Castro - a staunch Maduro ally.
Former foreign minister Delcy Rodriguez hailed this as a "constitution for peace and the sovereignty of Venezuela".
The Mexican government, critical of Maduro, called for the results of the opposition consultation to lead to a "negotiated solution" to help "restore" democracy.
It remains unclear what real impact the balloting - which the government dismissed as illegal and politically irrelevant - would have.
The elections council, which the opposition calls a pawn of Maduro, simultaneously held a test-run on Sunday for the July 30 vote to create the constitutional assembly.
Venezuela, with the largest proven oil reserves in the world, is nearly entirely reliant on its crude exports.
"Ten-year-old kids voted, thousands of minors, Australians, US citizens. a huge fraud", Socialist Party official Jorge Rodriguez said, mocking Sunday's vote which also took place among Venezuela's large diaspora communities.
Foreign Minister Samuel Moncada called a news conference to accuse global media of complicity with the opposition to exaggerate Sunday's vote and denigrate Maduro.
On Sunday, the opposition organized a popular referendum in which over 98 percent of 7.2 million voters said they opposed Maduro's proposal to call the Constituent Assembly. "We don't want to be a country without freedom", he added.
Opposition leaders said that was because they were able to set up only 2,000 polling places in a symbolic exercise the government labeled as illegitimate. More than 500 protesters and government opponents have been jailed.