On Monday, President Trump said the US stands behind opposition leader Juan Guaido and condemns Mr Maduro and his government’s socialist policies.
He pleaded with Venezuela’s military to abandon their support of Mr Maduro and said they should instead back Mr Guaido.
Mr Maduro responded by claiming the US president spoke in an “almost Nazi style” and mocked him for thinking he can give orders to Venezuela’s military.
“Who is the commander of the armed forces, Donald Trump from Miami?” Mr Maduro said on state TV. “They think they’re the owners of the country.”
Speaking at Florida International University in Miami in front of large American and Venezuelan flags, Mr Trump said “a new day is coming in Latin America”.
He said if Venezuela’s military continued to support Mr Maduro, ”you will find no safe harbor, no easy exit and no way out. You will lose everything.”
He added: “We seek a peaceful transition of power, but all options are open.”
The US, many of Venezuela’s neighbours and most Western countries have recognised Mr Guaido as Venezuela’s interim president.
But Mr Maduro, who won a second term last year in an election denounced by critics as a sham, has maintained the backing of Russia and China and his control of Venezuela’s state institutions, including the military.
It comes as Venezuela’s military blocked the US from moving tons of humanitarian aid airlifted in recent days to the Colombian border with Venezuela.
The aid shipments were intended in part to dramatise the hyperinflation and shortages of food causing so much strife in Venezuela.
Mr Trump said Mr Maduro “would rather see his people starve than give them aid”.