Updated

Costa Rica's president on Wednesday assured the nearly 5,000 Cuban migrants stuck in his Central American country that none of them will be returned to Cuba against their will.

The video message from President Luis Guillermo Solís came one day after the government of Belize rejected a Costa Rican proposal to fly the Cubans to that country. Belize said it would only participate within a regional arrangement.

For nearly a month, the Cubans have been accumulating in Costa Rica after Nicaragua, a close Cuba ally, closed its border to them. They are trying to reach the United States.

"Like you, I feel very disappointed that Guatemala, as well as Belize have denied passage through their territory to arrive in Mexico and from there continue on to your destination in the United States," Solís said. He said he would continue looking for a solution.

Some 45,000 Cubans are expected to move through South and Central American countries to the U.S. border this year. Cubans fear that the normalization of relations between their country and the U.S. could end the special immigration privileges they enjoy in the U.S.

Solís also asked the Cubans in Costa Rica to tell others who may be considering embarking on the same journey that now is not the time.

Solís was scheduled to begin an official visit to Cuba on Dec. 13, where he planned to discuss the topic with President Raúl Castro.

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