The warning comes a day after the opposition held a referendum to show the disapproval for the constituent assembly.
"The United States calls again on the holding of free and fair elections, and stand to the side of the venezuelan people in his quest to bring his country towards a full democracy and prosperity", added the american president.
Trump did not specify what measures could be taken.
Confrontation between the opposition and Maduro's government has left 96 people dead since April.
Since it lost control of parliament in the national vote in December 2015, the increasingly authoritarian government seems to have concluded that democratic elections are a luxury it can no longer afford.
Venezuelan President Nicolas Maduro (C) speaks with his ministers during meeting in Caracas on July 17, 2017.
"I won't be intimidated", Venezuela's president said in a speech at the presidential palace.
Colombian Foreign Minister Maria Angela Holguin said the Venezuelan crisis was discussed, but she denied reports that Santos traveled to convince Castro to act as a mediator.
Carried by the strong participation in this election, the venezuelan opposition on Monday launched a "final offensive" in an attempt to stop the project of the socialist president to change the Constitution, calling on them to support a 24-hour general strike on Thursday.
While Maduro is deeply unpopular - with 80 percent of Venezuelans criticizing his rein, according to the Datanalisis survey firm - he enjoys backing from some, mostly poor, parts of the population and, most importantly, from the military.
Maduro has rejected calls fora new presidential election before the scheduled 2018 vote.
REEVES: Well, that is the key question. Instead, the vote was organized on the fly by groups of volunteers: In just a couple of weeks, they set up 2,300 polling stations from the Amazon to the Atlantic coast.
More than seven million Venezuelans cast symbolic votes with 98 per cent rejecting President Maduro's plan, which the country's opposition says will create a virtual socialist dictatorship.
The current constitution, pushed through by Chavez in 1999, expanded the number of branches within the national government and consolidated the two houses of congress into a single body. "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 broadcast Monday. We are failing in other smaller states due to our economic vulnerability and entrenched political warfare: What makes us any more special with regard to Venezuela?
Authorities say several more trained dogs also will be part of the search today for Hector Garnica.
"The government must pull out its proposal of constitutional fraud". He probably is not even aware of the century we are living in, let alone with people around him and his inexplicably hypocritical stance with regard to funding the social experiment in Venezuela, tied to oil revenues.
Political analyst John Magdaleno told AFP that "there is evidence of a persistent and durable demand for political change".
Venezuela's opposition coalition has called for a general strike to take place on Thursday in protest over President Maduro's plans.
Former Mexican President Vicente Fox was banned from ever returning to the country, after acting as an observer in Sunday's non-binding referendum.