REYNOSA, Mexico — Hundreds of migrants are stuffed into the Senda de Vida shelter on the banks of the Rio Grande, a stone’s throw from Texas, waiting for a chance to claim asylum in the United States.

They say they want to do it the “right way” — by turning themselves in to U.S. authorities at the McAllen-Hidalgo International Bridge — rather than cross the river illegally. But many are growing tired of waiting weeks after putting their names on a list, maintained on the Mexican side and used to ration precious access to the nearby port of entry, that keeps getting longer as more and more people arrive from the south.

The Tribune's reporting for this project is supported by the Pulitzer Center.

Venezuelan Martin Gonzalez, traveling with his three kids, said he was told by U.S. Customs and Border Protection to come to Senda de Vida and “wait your turn.”

“What I’m asking for are my rights,” Gonzales said. “CBP told me, ‘Go to Senda de Vida, put your name on the list and wait your turn.’ And I’ve been waiting here 65 days.” Last week, he said, only 18 people were called to cross the bridge and make their asylum claims.

U.S. authorities say they only have so much capacity to process asylum-seeking migrants at ports of entry. According to a recent Politfact analysis, this practice of limiting entries, known as “metering,” has existed in some form at least since 2016, under the Obama administration.

The number of people who have to wait in Mexico is likely to grow significantly as the Trump administration moves to expand the so-called “remain in Mexico” policy. The program, in which asylum seekers must wait in Mexico while their cases move through backlogged U.S. immigration courts, began on the California-Mexico border before being extended to El Paso. Soon, officials expect migrants to be sent back to Nuevo Laredo, across the Rio Grande from Laredo, under the program, according to news reports.

Despite the risk of drowning or being taken against their will in Reynosa — the kidnapping capital of Mexico — some at Senda de Vida have given up waiting and have already left the relative safety of the shelter to press their luck at the bridges or crossing the river, migrants here said. Some said they have been waiting as long as three months.

Over the weekend, The Texas Tribune interviewed migrants from around the world — they had come from Central America, Cuba, Venezuela, Russia, Cameroon and even Bangladesh. Seven Bangladeshis at Senda de Vida, speaking in halting English, said they were kidnapped and robbed at gunpoint of everything they had — at least $700 and all their belongings — in Nuevo Laredo.

They pointed to cellphone pictures showing Mexican news reports of their capture and are now penniless, unsure of their next move.

“I want to go USA for save my life,” said Fokhrul Islam, one of the Bangladeshi migrants. “Help us, please. I request to immigration to help us.”

Not everyone at the shelter was impatient. A Russian man named Jason told the Tribune he is on the run from his government, which he said harasses members of his Libertarian Party. He arrived last Monday with his wife and said they were grateful to be safe inside the walls of Senda de Vida and planned to wait as long as it took to present their asylum requests.

“I stayed in line, and then get to the middle of the bridge,” he said. “I said I want to apply for political asylum, and they explained they had no room for new immigrants so I need to wait. That’s OK. It’s an understandable situation.”

Migrants at the shelter, along with its director, Hector Silva, say migrants are also facing extortion from corrupt Mexican authorities. They say friends and relatives who have crossed over told them they had to pay $1,200 to $1,500 to corrupt immigration agents for the chance to get to the bridge and claim asylum — a pattern the Tribune documented last year.

Emails sent to Mexico’s immigration agency and the Mexican Attorney General’s Investigation Unit for Crimes Against Migrants went unanswered.

Miguel Gutierrez Jr. contributed reporting to this story.