Mexican authorities for a second straight day Saturday refused mass entry to a caravan of Central American migrants held up at the border with Guatemala, but began accepting small groups for asylum processing and gave out some 45-day visitor permits that would theoretically allow recipients time to reach the United States.

Seeking to maintain order after a chaotic Friday in which thousands rushed across the border bridge only to be halted by a phalanx of officers in riot gear, authorities began handing out numbers for people to be processed in a strategy seen before at U.S. border posts when large numbers of migrants show up there.

Once they were processed, migrants were bused to an open-air, metal-roofed fairground in the nearby city of Tapachula, where the Red Cross set up small blue tents on the concrete floor. Easily 3,000 people or more the previous day, the crowd on the bridge thinned out noticeably.

But the slow pace frustrated those stuck on the bridge, where conditions were hot and cramped, and some pleaded at the main gate: “Please let us in, we want to work!” Behind it, workers erected tall steel riot barriers to channel people in an orderly fashion.

Each time a small side gate opened to allow small groups in for processing, there was a crush of bodies as migrants desperately pushed forward.

Scarleth Cruz hoisted a crying, sweat-soaked baby girl above the crowd, crying out: “This girl is suffocating.”

Cruz was among the many who appeared willing to accept any kind of migratory relief Mexico might offer. Cruz, 20, said she was going to ask for political asylum because of threats and repression she faced back in Honduras from President Juan Orlando Hernandez’s governing party.

“Why would I want to go to the United States if I’m going to be persecuted” there as well, she said.

Mexico’s Interior Department said in a statement that it had received 640 refugee requests by Hondurans at the border crossing. It released photos of migrants getting off buses at a shelter and receiving food and medical attention.

At least a half-dozen migrants fainted amid the heat, and a steady stream abandoned the bridge to cross the Suchiate River by swimming, fording its shallows with the aid of ropes or floating in groups of about 10 on rickety rafts. None were visibly detained despite the presence of hundreds of police lining the bridge.

Some migrants tore open a fence on the Guatemala side of the bridge and threw two young children, perhaps age 6 or 7, and their mother into the muddy waters about 40 feet below. They were rafted to safety in on the Mexican bank.

Some on the bank yelled warnings to migrants on the bridge not to get on buses organized by Mexican authorities, claiming it was a ruse to deport them. There was no evidence of anyone being deported through such trickery, but the warnings made plenty leery of boarding, like Fidelina Vasquez, a grandmother traveling with her daughter and 2-year-old grandson.

A Mexican migration official who declined to give his name because he was not authorized to discuss the matter publicly said that between Friday and Saturday, authorities had deported by bus about 500 people who voluntarily decided to return.

Migrants have commonly cited widespread poverty and gang violence in Honduras, one of the world’s deadliest nations by homicide rate, as their reasons for joining the caravan.

“One cannot live back there,” Vasquez said, standing next to the main border gate.

Hector Aguilar, a 49-year-old sales manager who worked as a taxi driver in Honduras’ Yoro province to feed his four children, said he had to pay the two main gangs there protection money in order to work.

“On Thursdays I paid the 18th Street gang, and on Saturdays the MS-13,” Aguilar said. “Three hundred lempiras per day” — about $12.50, a significant amount in low-wage Honduras.

At the gate, Mexican workers handed food and water to the migrants. Through the bars, a doctor gave medical attention to a woman who feared her young son was running a fever.

Some migrants returned to Tecun Uman on the Guatemalan side to buy food and supplies. Local women brought water for the migrants to bathe.

The caravan elicited a series of angry tweets and warnings from U.S. President Donald Trump early in the week, but Mexico’s no-nonsense handling of the migrants at it southern border seems to have satisfied him more recently.

“So as of this moment, I thank Mexico,” Trump said Friday at an event in Scottsdale, Arizona. “I hope they continue. But as of this moment, I thank Mexico. If that doesn’t work out, we’re calling up the military — not the Guard.”

He also warned the migrants that they should turn back.

“They’re not coming into this country,” said Trump, who has sought to make the caravan and border security in general a campaign issue for Republicans ahead of the U.S. midterm elections.

Also Friday, U.S. Secretary of State Mike Pompeo met in Mexico City with his Mexican counterpart, Luis Videgaray, with the caravan high on their agenda.

“The Mexican Government is fully engaged in finding a solution that encourages safe, secure, and orderly migration,” State Department Spokeswoman Heather Nauert said Saturday, “and both the United States and Mexico continue to work with Central American governments to address the economic, security, and governance drivers of illegal immigration.”

Mexican President Enrique Pena Nieto said late Friday that “Mexico does not permit and will not permit entry into its territory in an irregular fashion, much less in a violent fashion.”

Presidents Hernandez of Honduras and Jimmy Morales of Guatemala held an emergency meeting Saturday at a Guatemalan air base.

The leaders said an estimated 5,400 migrants had entered Guatemala since the caravan was announced a week ago, and about 2,000 Hondurans have returned voluntarily. Both leaders had spoken by phone with Pena Nieto and U.S. Vice President Mike Pence to discuss humanitarian aid and efforts to help people who want to return.

Morales said a Honduran migrant died in the town of Villa Nueva, about 20 miles (30 kilometers) from Guatemala City, when he fell from a truck that was transporting migrants.

Thousands of migrants slept — or tried to sleep — outdoors overnight underneath tarps and what blankets were available. They awoke amid trash and an unpleasant smell, as some had no choice but to relieve themselves in the same area.

Jose Yanez, said he woke up at 5 a.m. with a backache after having nothing to cover himself from the nighttime chill. But the 25-year-old farmer was determined to press onward, explaining that the $6 a day he made back home was not enough to live on.

“From here,” Yanez said, “there’s no going back.”

(AP)