Maduro attempted to begin dialogue with Washington and requested a phone call with Trump on Friday. The Peruvian leader, a former Wall Street investor who spent decades living in the USA, is frequently mocked on Venezuelan state TV and was once even called the "empire's lapdog" by the country's foreign minister.
Trump did not specify what type of options he had in mind.
Washington has slapped sanctions on President Nicolas Maduro and some of his allies, and branded him a "dictator" over his attempts to crush his country's opposition. "Mr. Lopez and Mr. Ledezma are political prisoners being held illegally by the regime", Trump said in a statement earlier this month, referencing Leopoldo Lopez and Antonio Ledezma, two of Maduro's top political opponents. Mexico and Colombia joined in with statements of their own.
The countries expressed their solidarity in a public declaration in which they congratulated Venezuela on the Constituent Assembly and rejected mounting global attacks against the country.
"We have many options for Venezuela and by the way, I'm not going to rule out a military option", Trump told reporters at his golf club in Bedminster, New Jersey. He has been accused of setting up a powerful constitutional assembly to push aside opposition. On Friday, Peru expelled Venezuela's ambassador. Argentina's foreign minister said Mercosur countries also reject the use of force.
Assembly members said the decision was made in part because the election had been delayed due to "opposition-led violence".
Violent demonstrations since April have left more than 120 people dead.
The National Electoral Council (CNE) was asked by the assembly to set the exact date for the governors' election.
Protests have rocked the streets of Caracas and other Venezuelan cities, both before the vote and in response to the recent political moves.
"With this extremist elite that's in charge in the United States, who knows what will happen to the world?"
Previous U.S. administrations had brushed this off as politicized rhetoric meant to distract from Venezuela's domestic problems.
The Venezuelan government had previously responded to the sanctions - which already targeted Maduro himself - by saying the USA was "making a fool of itself in front of the world".
Venezuela's Information Minister Vladimir Villegas on Saturday tweeted a picture of the Statue of Liberty holding a machine gun instead of a torch, and a link to an article describing, "A Chronology of U.S".
Trump said a military option was "certainly something that we could pursue".