President Bush on Wednesday said he was following in another president's footsteps — John F. Kennedy's — setting out a new policy toward Cuba that calls for international community assistance in bringing democracy to the communist country.

"In this building, President John F. Kennedy spoke about the U.S. economic embargo against Cuba's dictatorship. And it was here where he announced the end of the missile crisis that almost plunged the world into nuclear war," Bush said at the State Department, where Kennedy announced the successful end to the 1962 Cuban Missile Crisis.

"Today, another president comes, with hope, to discuss a new era for the United States and Cuba. The day is coming when the Cuban people will chart their own course for a better life," he continued.

Bush seized on leader Fidel Castro's fading health as a chance for rare change, and asked other nations to help Cuba eventually become a free society by committing money and political capital to the cause.

The speech is Bush's first stand-alone address on Cuba in four years. He was joined on stage by families of Cuban dissidents, whom he referenced to show the lack of freedoms by Castro's regime.

"I ask that God watch over you and your loved ones," Bush told the family members, repeating the same message in Spanish.

Bush said the Cuban regime leaders had promised freedom when they first took over, but they did not follow through on their promise.

"The socialist paradise is a tropical gulag. ... And as with all totalitarian systems, Cuba's regime no doubt has other horrors still unknown to the rest of the world. Once revealed, they will shock the conscience of humanity, and they will shame the regime's defenders and all those democracies that had been silent," Bush said.

Bush looked to the day when Castro is gone, describing a nation in which Cuban people choose a representative government and enjoy basic freedoms, with support from a broad international coalition.

"Now is the time to support democratic movements growing on the island. Now is the time to stand with the Cuban people as they stand up for their liberty. And now is the time for the world to put aside its differences and prepare for Cuba's transition to a future of freedom and progress and promise," Bush said.

Challenging the nearly 50-year-old dictatorship, the president said today's dissidents will be tomorrow's leaders.

"When freedom finally comes, they will surely remember who stood with them," he said.

The president called on Congress to maintain the trade embargo on Cuba until it changes its ways, saying that Cuba has used the embargo as a scapegoat. Washington's decades-old embargo prohibits U.S. tourists from visiting the island and chokes off nearly all trade between both countries. As a result of the hardship it creates, some lawmakers have asked for a reassessment of its purpose and success.

Bush said that trade with Cuba only would empower the current government and the country's elites.

"As long as the regime maintains its monopoly over the political and economic right of the Cuban people, the United States will keep the embargo in place," Bush said.

In Cuba, Castro, 81, remains the island's unchallenged leader. But the ailing president, who accuses Bush of being obsessed with Cuba and threatening humanity with nuclear war, is rarely seen in public anymore.

Life has changed little on the island under the authority of his brother, 76-year-old Raul Castro, who has been his elder brother's hand-chosen successor for decades. Still, municipal elections held Sunday were the first step in a process that will determine if Castro is re-elected or replaced next year. The Communist Party is the only participant allowed, and while candidates do not have to be members, critics claim they are the only ones who ever win.

In a direct appeal to ordinary citizens in Cuba, Bush told Cubans they have the power to change their country. The White House says that is not meant to be a call for armed rebellion.

"Su dia ya viene llegando," Bush repeated several times, which in English means, "Your day is coming soon."

The president urged dissidents to step up efforts on the island and send a message to the Cuban military and police that they do not have to go down with the regime.

Bush proposed new initiatives to follow through on his call: the creation of an international "freedom fund" to help Cuba's potential rebuilding of its country one day; a U.S. licensing of private groups to provide Internet access to Cuban students; and an invitation to Cuban youth to join a scholarship program.

The latter two offerings help the Bush administration underscore the kind of real-life limitations that Cubans now face — from blocked Internet access to restricted information about their leaders to denial of legal protections. The creation of the international fund is meant to speed up societal transformation.

FOX News' Bret Baier contributed to this report.