Costa Rican President Luis Guillermo Solis admits that stranded Cuban migrants in their territory will soon need to move on as his government can no longer support.

A report from Reuters on Sunday disclosed how Solis is planning to tell Cuban President Raul Castro to push for a resolution of the long-standing migrant crisis because Costa Rica cannot keep caring for the Cubans in their territory.

"We cannot maintain this task indefinitely. With all brotherly frankness, I will pose this in meetings to be held with the presidents of the SICA (Central American Integration System) and in Havana with President Raul Castro," Solis admitted in a state broadcast seen all over in Costa Rica.

According to the report, Solis is due to tell this to Cuban President Raul Castro on Tuesday during the regular conventions of the Central American Integration System, or SICA, where leaders of both countries will be in attendance.

According to CNN, about 5,000 Cubans who wish to migrate to the U.S. to live the "American Dream" were stalled at the border of Costa Rica and Nicaragua after the latter, as well as Guatemala, refused to allow them to have free transit through their territories.

TelSUR noted how at the beginning of their journey, the Cubans were under the impression that they would be welcomed with open arms in the U.S. because of Washington's Cuban Adjustment Act of 1966 or the so-called "wet-foot, dry-foot" policy.

The policy, which paved the way for eased travel restrictions in Cuba, allowed many with the opportunity to leave their home country for the first in decades, says CNN.

The report also noted how Solis eased the minds of some, via a video message upload, for those who were worried that they would be sent home by the Costa Rican government.

"Some of you are worried that the government of Costa Rica might negotiate a forced return of all of you to Cuba. That's not going to happen. I'm not going to do that," CNN translated his statement.

According to Reuters, Costa Rica closed its borders after capturing smugglers and provided Cubans temporary visas to pass through their country.

This did not go unappreciated as some of the migrants at the San Ramon shelter interviewed by CNN lauded the act of kindness.

"We would like to thank Costa Rica for everything it has done for us, the help for children, the elderly and pregnant women; but we don't want to stay in Costa Rica. We want to go on toward the United States," Ivan Oliva told CNN.