La Cruz (Costa Rica) (AFP) - A protest by desperate Cuban migrants stranded on their journey to the United States paralyzed a key border crossing between Costa Rica and Nicaragua Tuesday.

Long lines of buses and trucks formed on both sides of the frontier as the migrants refused to let traffic pass, authorities from the two countries said.

"The international transport of passengers and cargo remains paralyzed" at the Penas Blancas border post, the Nicaraguan government said, warning of disruptions to trade and transport "for the entire Central American region."

A spokesman for Costa Rica's immigration authority confirmed the blockage.

More than 2,000 Cubans are stuck at the border, penniless and without immigration papers.

Many were stranded when Costa Rica busted a human trafficking ring that was charging $7,000 to $15,000 (6,500 to 14,000 euros) to smuggle them into the United States.

They are part of a growing surge in Cubans trying to reach the United States since Washington and Havana announced a thaw in their Cold War-era standoff last December.

For Cubans looking to leave the communist island, the rapprochement has sparked fears that the US policy of granting asylum to Cuban arrivals may be near an end.

Rather than risk the trip by boat across the Florida Straits, where the US Coast Guard can send them back, many now fly to Ecuador, which does not require visas for Cuban nationals.

Then they work their way north, overland and by boat.

- Increasingly desperate -

In Santa Cruz, on the Costa Rican side of the border, the increasingly desperate Cubans are being housed in churches, community centers and gyms.

They pass the time sprawled on mattresses on the shelter floors or drinking coffee served from large green buckets by volunteers.

Many described being trapped in limbo, uncertain of their fate.

"I don't think Nicaragua is going to open its doors to us. We don't know what's going to happen to us. We could be here five days, 10 days, but I don't think we can take much more," said Yordani Garcia, 32.

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He is determined not to go back. "Things in Cuba aren't getting any better. On the contrary, they're getting worse," he said.

Santa Cruz community leaders have mobilized to take in the stranded migrants with the help of government funds. But the Cubans are all too aware of the burden they pose.

"We don't know if we'll be able to stay much longer. It's a big expense for Costa Rica," said Dayana Gonzalez, 28, who is traveling with her eight-year-old daughter, her sister and two nieces, aged eight and 10.

- Surge of Cubans -

Costa Rica called for an urgent meeting of foreign ministers along the Cubans' route, from Ecuador to Mexico.

Foreign Minister Manuel Gonzalez said the countries need to establish a "humanitarian corridor" to prevent would-be migrants falling into the hands of human traffickers.

There was a 78-percent increase in Cubans arriving in the United States in the nine months to July 2015, to 27,296 people, according to the Pew Research Center, citing official US figures.

Two-thirds of them arrived through Laredo, Texas, on the Mexican border -- 66 percent more than last year.

The Cubans stranded in Central America have sparked a diplomatic row between Costa Rica and Nicaragua, which already have two border disputes pending at the International Court of Justice.

Costa Rica gave the Cubans temporary visas so they could continue their journey north, but Nicaragua irately sent them back, accusing its southern neighbor of "deliberately and irresponsibly" sparking a humanitarian crisis.

On Sunday, Nicaragua deported hundreds of Cubans it said had crossed the border "by force."

Costa Rica for its part criticized Nicaragua for using the army to expel the migrants with tear gas and rubber bullets.

Havana Tuesday said it was in "constant contact" with authorities in both Nicaragua and Costa Rica, "with the aim to find a swift and adequate solution, which takes the well-being of Cuban citizens into consideration."

It also emphasized that the Cubans were welcome to return home to the communist island.

However the situation also encompasses larger geopolitical considerations.

Costa Rica's government has long been close to the United States, while Nicaraguan President Daniel Ortega is a staunch ally of Cuba dating back to 1979, when his Sandinista rebels overthrew Nicaragua's US-backed government.

Ortega, who was installed at the head of a junta government, stepped down in 1990. He has been back since 2007 as the country's elected president.