(USA TODAY) - President Trump told cheering Cuban-Americans on Friday that his new restrictions on U.S. travel to and business dealings with the island will help bring down the communist regime.

"With God's help, a free Cuba is what we will soon achieve," Trump said in unveiling plans that reverse some of the revamped Cuba policies made by predecessor, President Barack Obama.

The current Cuban regime has been in place since 1959 and weathered a U.S. economic embargo from 1962 to last year, when some of the restrictions were lifted.

Trump is not reversing all of Obama's Cuba policy; the two nations, for example, will still have re-opened embassies in their capital cities.

Critics said the Trump restrictions will undermine the president's goal of a free Cuba, and that increased exchanges would do more to encourage an overthrow of the government in Havana.

Bipartisan criticism

"These policy changes by President Trump will only take us back toward a Cold War policy that was a miserable failure and held our country back for more than 50 years," said Rep. Jim McGovern, D-Mass.

A Republican senator, Jerry Moran of Kansas, questioned Trump's plans to restrict sale of U.S. products to Cuba, saying the island nation "is a natural market for our nation’s farmers and ranchers — and when we don’t sell to Cuba, another country does."

Borrowing a Trump campaign phrase, Moran said "putting America first means exporting what we produce to countries across the globe."

In his remarks, Trump said the Obama administration's "terrible and misguided deal" benefits only the Castro regime rather than the people it addresses. He said the regime, founded by Fidel Castro and now run by brother Raul, has spread "violence and instability" throughout the region.

Trump pledged to keep the economic embargo on Cuba until it releases political prisoners and allows political parties and freedom of assembly.

The crowd included Cuban-Americans whose families left the island after Fidel Castro took over the government in 1959, overthrowing the dictatorship of Fulgencio Batista.

Citing "wonderful memories" from campaign visits, Trump said "that was right before the election -- I guess it worked."

The president also met privately with veterans from the Bay of Pigs, the ill-fated April 1961 invasion of Cuba by Cuban exiles and backed by the CIA.

He was pushed by Florida Republicans, including senator and former primary opponent Marco Rubio.

Addressing the crowd ahead of Trump, Rubio said "this change empowers the people of Cuba," adding that "we will not empower their oppressors."

Vice President Pence said that "America stands with the persecuted, the oppressed, and the exploited in Cuba."

Polls conducted last December showed that 75% of Americans favored the change in policy toward Cuba.