SAN PEDRO SULA, Honduras (Reuters) - The Organization of American States lifted its 47-year suspension of Cuba on Wednesday in a move backed by Washington as it tries to soothe Cold War tensions with the communist-run island.

The 34-member hemispheric body, meeting in Honduras, unanimously scrapped a 1962 decision at the height of the Cold War that barred Cuba as revolutionary leader Fidel Castro took it toward communism and an alliance with the Soviet Union.

While leftists in Latin America hailed the OAS vote as a diplomatic victory for Cuba, Washington said it had succeeded in ensuring that Cuba cannot rejoin the group without moving toward democracy and respect for human rights.

U.S. President Barack Obama has taken steps toward a more open relationship with Cuba, lifting restrictions on travel and cash remittances to Cuba for Cuban-Americans with relatives on the island.

But his administration had said Havana should not be allowed to return to the OAS until it embraces democratic principles and makes progress on human rights.

Cuba’s allies in Latin America instead called for Cuba to be allowed back in from the cold with no conditions, and Secretary of State Hillary Clinton came under heavy pressure at the OAS meeting here this week.

In a diplomatic compromise, the group’s member countries agreed that Cuba’s re-entry would be “the result of a process of dialogue” which Cuba has to request and must be in line with OAS principles.

Clinton said Cuba’s return to the group -- which is little known in the United States and Canada but carries diplomatic weight in Latin America -- would now “turn on Cuba’s commitment to the organization’s values.”

That was a reference to the OAS’s commitment to defend democracy and human rights under a 2001 Democratic Charter.

“I am pleased that everyone came to agree that Cuba cannot simply take its seat and that we must put Cuba’s participation to a determination down the road - if it ever chooses to seek reentry,” she said.

NO WORD FROM CUBA

In Havana, there was no immediate government reaction to the island’s acceptance back into the fold of the OAS.

“It’s good news because it means things continue to loosen up, but the government isn’t going to stand back now and say the OAS is good. I’m sure they’re won’t ask for re-entry to the organization,” said Daniel Rodriguez, a professor in Havana.

Cuba has repeatedly said it has no interest in returning to the OAS. Before the OAS vote, former Cuban leader Fidel Castro described the body as an “accomplice” to crimes against Cuba, including a U.S. economic embargo.

But Cuba’s leftist allies in the region had pushed for the suspension to be lifted and treated the vote as a diplomatic victory for Cuba.

“The Cold War has ended today here in San Pedro Sula. We have made a wise and honorable decision,” Honduran President Manuel Zelaya said.

Despite opening up to Cuba, Obama has refused to drop the decades-old embargo on the island, saying its communist leaders need to free political prisoners and improve human rights.

U.S. officials sought to cast the outcome as a victory, arguing they had staved off the possibility of the OAS simply throwing open its arms to Cuba by rescinding the suspension without any insistence on democracy and human rights.

“The ball is now in Cuba’s court to abide by the principles of human rights and democracy embodied in the Inter-American Democratic Charter,” said Representative Eliot Engel, chairs of the Foreign Affairs Subcommittee on the Western Hemisphere.

Staunch opponents of the Cuban government in the Cuban American community were not happy with the OAS decision.

U.S. Representative Ileana Ros-Lehtinen, the ranking Republican on the House Foreign Affairs Committee, from Miami, called it “an affront to the Cuban people and to all who struggle for freedom, democracy and fundamental human rights.”

“Rather than upholding democratic principles and fundamental freedoms, OAS member states, led by the OAS Secretary General, could not move quickly enough to appease their tyrannical idols in Cuba,” Ros-Lehtinen said.

The OAS move could allow Cuba to request loans from the Inter-American Development Bank although it was not clear if it would first have to apply for membership or if the lifting of the suspension would be enough.