Venezuela is plunging deeper into a political chaos triggered by the USA demand that Maduro step down a month into a second presidential term that the US and its allies in Latin America consider illegitimate.
Speaking at Florida International University in Miami before large American and Venezuelan flags, Trump said the US stands behind Guaido, whom the USA recognizes as the country's rightful president, and condemns President Nicolas Maduro's government and its socialist policies.
And while he avoided tying Democratic politicians to the socialist government in Venezuela as he has in the past, Trump briefly turned his speech on Venezuela to domestic politics, vowing the U.S. will "never be a socialist country".
Earlier the White House said Trump would use the speech to warn of "the dangers of socialism".
The staying power and vested interests of the Venezuelan military, which is backing Maduro's government, remain a barrier to change, the official said.
The military has blocked the US from moving tons of humanitarian aid airlifted in recent days to the Colombian border with Venezuela.
Despite declaring himself interim president last month and being recognized by the US, Guaido ultimately has no say over whether the aid is allowed in.
"We seek a peaceful transition of power, but all options are open", Trump said.
Maduro responded to Trump in comments broadcast on state television in which he criticized the US president of speaking in an "almost Nazi style" and lashed out at him for thinking he can deliver orders to Venezuela's military.
"And to those who would try to impose socialism on the United States, we again deliver a very simple message: America will never be a socialist country", Trump said toward the end of his speech.
Critics say Maduro's re-election a year ago was fraudulent, making his second term illegal.
In Caracas, Guaido, whose claim to be interim president now has the support of more than 50 countries, told a large rally that 600,000 people had registered to help bring desperately needed aid in through border points. He has since garnered broad support, calling massive street protests and winning recognition from the USA and dozens of nations in Latin America and Europe who share his goal of removing Maduro.
Maduro reportedly extended an invitation to meet with the U.S. special envoy on Venezuela, Elliott Abrams.
Trump spoke on Monday in Miami about the political crisis in Venezuela and the dangers of socialism.
Trump urged the Venezuelan military to accept Guaido's offer of amnesty and refrain from violence against those opposing Maduro's government. Sanders says Trump would warn the Venezuelan military that the USA "knows where military officials and their families have money hidden throughout the world".
Trump has also previously seized on the deteriorating situation in Venezuela as a political attack line, warning voters in hyperbolic terms that Democratic policies will turn the U.S. into Venezuela. He said that it "is not new" that Maduro holds out hope of meeting the US president, but it reflects a realization that his crisis-riddled nation rejects his "model of governance".
Two senior Venezuelan officials who were not authorized to discuss the meetings publicly said the two encounters between Abrams and Foreign Minister Jorge Arreaza came at the request of the U.S.
"I talked to Juan Guaido, and the team, the people around him, to see what could be most helpful", Branson said.