Dese Washington, White House sources have confirmed that the change of policy towards Cuba also includes its support for the trade and financial embargo on the island and, therefore, the frontal opposition to worldwide requests for Congress to lift it.
In Miami, Trump reiterated support for the United States' 1961 trade embargo against Cuba - which has been the most harmful USA provision against Havana since diplomatic relations soured with the revolution that put former dictator Fidel Castro in power.
Trump is challenging Cuba to negotiate better agreements for Americans, Cubans and those whose identities lie somewhere in between.
(AP Photo/Evan Vucci). President Donald Trump speaks about Cuba policy, Friday, June 16, 2017, in Miami.
"America has rejected the Cuban people's oppressors", Mr Trump said in a crowded, sweltering auditorium.
In Havana, Cuba's government criticised the new restrictions on ties with the United States that were announced by Trump, but reiterated its willingness to hold a "respectful dialogue" with Washington.
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The reversal of policy changes enacted by former President Barack Obama were touted by President Trump as an inspiration for those citizens of that nation to embrace new "political and economic freedoms". Diplomatic relations will remain in tact and commercial air and sea links will be exempted from the new restrictions. Yet, by returning to the failed policy of the past 55 years, the Administration moves no closer to helping improve the human rights situation in Cuba and stands to violate the President's number one campaign promise and constitutional responsibility- to keep the American people and our homeland safe.
Trump also demanded the return of US fugitives including Joanne Chesimard, a black militant convicted in 1977 of the murder of a New Jersey state trooper.
"This is the simple truth of the Castro regime", Trump said. "He takes a different tack depending on the nature of the relationship between the two countries, but his concern is consistent no matter what the country".
"When he's cutting back on travel, he's hurting us, the Cuban entrepreneurs", said Camilo Diaz, a 44-year-old waiter in a restaurant in Havana.
Trump's proposed policy could stifle hotel development on the island and ban Americans from staying at hotels with ties to the Cuban military. "We will enforce the embargo", the United States president said. "I support President Trump 100 percent".
Most U.S. travelers to Cuba will again be required to visit the island as part of organized tour groups run by American companies.
"This is a hollow retreat from normalization that takes a swipe at Americans' freedom to travel, at our national interest, and at the people of Cuba who yearn to reconnect with us - all just to score a political favor with a small and dwindling faction here at home", Leahy wrote.More news: Trump Appears to Confirm He Is Under Federal Investigation
Holidaymakers from the USA will be restricted to package tours organised by United States firms - unlike British tourists who can stay in bed-and-breakfast hotels and wander the streets of Havana.
As a result, the changes - though far-reaching - appear to be less sweeping than many U.S.pro-engagement advocates had feared.
"The government of Cuba denounces the new measures toughening the embargo" imposed since 1962, according to the statement.
"I do believe that end is in the very near future", he said.
The Obama administration had restored diplomatic relations with its Cold War foe in December 2014.
Weissenstein reported from Havana and Lederman from Washington.More news: Wounded US lawmaker 'in some trouble', Trump says
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