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Speaking to a cheering crowd mostly of Venezuelan and Cuban immigrants in Miami, Trump said if the Venezuelan military continues supporting Maduro, "You will find no safe harbour, no easy exit and no way out. You’ll lose everything.”
Maduro retaliated late on Monday that Trump's speech was "Nazi-style" and said he acted as if he were the owner of Venezuela and its citizens his slaves.
Trump offered strong backing for Venezuelan opposition leader Juan Guaido, whom the United States, many of Venezuela's neighbours and most Western countries have recognised as interim president of Venezuela.
But Maduro, who won a second term last year in an election that critics denounced as a sham, retains the backing of Russia and China and control of Venezuelan state institutions, including the security services.
Trump cautioned Venezuelan armed forces not to harm Guaido or other opposition politicians, urged them to accept the National Assembly leader's offer of amnesty and demanded that they allow in food, medicine and other supplies.
Guaido, who invoked constitutional provisions to declare himself the country's leader last month, has said that aid will enter Venezuela from neighboring countries by land and sea on Saturday.
The United States has sent tonnes of aid that is being stockpiled on Colombia's border with Venezuela, but Maduro has refused to let it in.
Maduro calls the aid a US-orchestrated show and denies any crisis despite many Venezuelans' scant access to food and medicine.
"We will not make of the honourable Venezuela a Venezuela of beggars," he said in televised comments on Monday. "We will not accept it."
Maduro said Venezuela already received "humanitarian assistance" on a daily basis. Russia, for example, was sending 300 tonnes of aid to the country by plane on Wednesday, he said, albeit clarifying this was not a donation but supplies for which Venezuela had paid.
BROAD ATTACK ON SOCIALISM
“We seek a peaceful transition of power but all options are open," Trump said. It was a further hint of Trump's repeated insistence that military options remain on the table, though most Latin America experts believe such action is unlikely.
The United States has had direct communications with members of Venezuela's military urging them to abandon Maduro, a senior White House official told Reuters this month, and Trump's aides have openly predicted more defections.
But so far, few military officers have turned against Maduro.
A source in Washington close to the opposition expressed doubts whether the Trump administration has done sufficient groundwork to spur a wider mutiny in the ranks, where many officers are suspected of benefiting from corruption and drug trafficking.
Guaido, in a videotaped message to the crowd at Florida International University, called it a "decisive moment" to exert pressure on Maduro from inside and outside the country.
Trump also used his speech to rail against socialism as a "dying" ideology in the Western Hemisphere and to brand Maduro a "puppet" of communist-ruled Cuba.
While the Republican president did not directly equate socialism with the Democratic party, as he appeared to do in his State of the Union speech this month, he alluded to his earlier criticism of domestic policies proposed by some liberal Democrats.
"America will never be a socialist country," he said.
Trump wants to boost support among Florida's Hispanic voters as he looks ahead to his re-election campaign in 2020, when Florida is again expected to be an important swing state.