HAVANA (Reuters) - U.S. President Barack Obama challenged Cuba’s Communist government with an impassioned call for democracy and economic reforms on Tuesday, addressing the Cuban people directly in a historic speech broadcast throughout the island.

Taking the stage at Havana’s Grand Theater with President Raul Castro in attendance, Obama said he was in Cuba to extend a hand of friendship and “bury the last remnant” of the Cold War in the Americas.

But he also pressed hard for economic and political reforms and greater openness in a one-party state where the government stifles dissent, Internet access is low and the media is in state hands.

His speech was the high point of a 48-hour trip made possible by his agreement with Castro in December 2014 to cast aside decades of hostility that began soon after Cuba’s 1959 revolution, and work to normalize relations.

Nonetheless, Obama threw down a very public gauntlet to Castro, saying Cubans cannot realize their full potential if his government does not allow change and relax its grip on Cuban politics and society.

“I believe citizens should be free to speak their minds without fear,” Obama told the audience on the final day of his visit. “Voters should be able to choose their governments in free and democratic elections.”

“Not everybody agrees with me on this, not everybody agrees with the American people on this but I believe those human rights are universal. I believe they’re the rights of the American people, the Cuban people and people around the world,” Obama said.

The hand-picked audience cheered him repeatedly, especially when he criticized the longstanding U.S. economic embargo against Cuba, spoke glowingly of Cubans’ talents and praised the country’s achievements in healthcare and education.

The spectacle of the leader of the United States, the superpower to the north for long reviled by Cuba’s government, standing in Havana and urging such changes in a speech broadcast into homes across the island would have been unthinkable before the two countries began their rapprochement 15 months ago.

Since then, Obama has repeatedly used his executive powers to relax trade and travel restrictions, while also pushing Cuba to accelerate cautious market-style reforms introduced by Castro and allow greater political and economic freedom.

Castro has welcomed Obama’s moves while insisting that a new relationship with the old enemy does not mean Cuba plans to change its political system.

The audience of more than 1,000 people at Obama’s speech on Tuesday included officials and business people from both countries, U.S. lawmakers and members of Cuba’s cultural elite.

Obama drew sustained applause when he reiterated his call for the U.S. Congress to lift the embargo, which he called “an outdated burden on the Cuban people.”

But the response was more muted when he challenged Castro to allow greater political liberties.

Obama went straight from the speech to a private meeting with prominent dissidents on the island, a few of whom object to his engagement policy.

“As far as I am concerned nothing has changed, the repression continues,” said Berta Soler from the Ladies in White group, who met Obama at the embassy.

Cuba’s government dismisses the dissidents as mercenaries without public support but Obama applauded their work and “extraordinary courage.”

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Obama sees his dramatic shift away from a decades-old policy of trying to isolate and weaken Cuba as a success story and wants to make it an irreversible part of his legacy by the time he leaves office in January.

Still, major obstacles remain to full normalization of ties, notably the differences over human rights, the Republican-controlled U.S. Congress’ refusal to lift the embargo and Washington’s resistance to discussing the return of the U.S. naval base at Guantanamo Bay, Cuba.

Obama’s critics at home have criticized his visit to Cuba as a premature reward to the Communist government. U.S. House of Representatives Speaker Paul Ryan, a Republican, said on Tuesday the trip legitimizes what he called Castro’s “tyrannical dictatorship.”

‘IT’S UP TO YOU’

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With his words carried live by Cuba’s state-run media, Obama sought to persuade ordinary Cubans that his new policy was focused primarily on helping them to improve their lives.

Standing at a lectern flanked by U.S. and Cuban flags, he laid out a hopeful vision of future relations and told Cubans “it’s up to you” to take steps to change the country.

Obama pointedly stopped short of what some of his critics had demanded – that he echo U.S. President Ronald Reagan’s famous exhortation in a 1987 speech in West Berlin for Soviet leader Mikhail Gorbachev to tear down the Berlin Wall.

But he did encourage Cubans to embrace democracy, set up their own businesses and help improve Cuban society.

“Many suggested that I come here and ask the people of Cuba to tear something down. But I’m appealing to the young people of Cuba who will lift something up, build something new,” he said.

Some Cubans who saw the speech in their homes or local cafes were also impressed by his frank admission of America’s own failings.

“He has been very honest in his statements,” said Santiago Rodriguez, 78, in his home in central Havana. “It is not only the blockade (embargo) that has overwhelmed us for years. This was a message full of suggestions and positive criticism for the future of Cuba.”

Castro, an army general who took over as president from his ailing brother, Fidel Castro, in 2008, was at the theater to greet Obama on arrival and sat in the audience for the speech. At the end, he lightly applauded from the balcony, then waved to the crowd.

Later, the two leaders entered together to loud applause at Havana’s Latin American Stadium and sat side-by-side for a baseball game between Cuba’s much-loved national team and Major League Baseball’s Tampa Bay Rays.

Castro was also on hand at the airport to bid Obama farewell, giving him an enthusiastic handshake at the bottom of Air Force One’s stairway and then exchanging waves once the U.S. leader reached the top.

After the two men met on Monday, they aired some of the old grievances between their countries at a joint news conference, even as they sought to advance the diplomatic thaw.

Obama’s administration is seeking to galvanize the Cuban people to help him pressure their government for reforms. But flashes of anger from Castro at the news conference illustrated how Washington runs the risk of being accused of meddling.

Obama’s address on Tuesday was the first time a sitting U.S. president’s speech was broadcast to the Cuban people while on Cuban soil – although speeches by visiting popes have been carried live by state media.

Jimmy Carter, traveling to Cuba in 2002 as the first former U.S. president to visit since the revolution, also called for political freedoms in a speech broadcast on live television.