CIUDAD HIDALGO, Mexico — A growing throng of Central American migrants resumed their advance toward the U.S. border in southern Mexico on Sunday, overwhelming Mexican government attempts to stop them at the border.

Their numbers swelled to about 5,000 overnight, and at first light they set out walking toward the Mexican town of Tapachula, 10 abreast in a line stretching about a mile.

Several hundred more already had applied for refugee status in Mexico, and an estimated 1,500 were still on the Guatemalan side of the Suchiate River, hoping to enter legally.

It was not immediately clear where the additional travelers had materialized from since about 2,000 had been gathered on the Mexican side Saturday night. They seemed likely to be people who had been waiting in the Guatemalan town of Tecun Uman and who decided to cross during the night.

As they passed through Mexican villages on the outskirts of Ciudad Hidalgo, they drew applause, cheers and donations of food and clothing from Mexicans.

Maria Teresa Orellana, a resident of the neighborhood of Lorenzo, handed out free sandals to the migrants as they passed. “It’s solidarity,” she said. “They’re our brothers.”

In the tropical heat, Besi Jaqueline Lopez of San Pedro Sula carried an improbable stuffed polar bear with a winter cap, the favorite — and only — toy of her two daughters, Victoria, 4, and Elisabeth, 3, as they trudged beside her.

A business administration graduate, Lopez said she couldn’t find work in Honduras. She wants to reach the United States but would stay in Mexico if she could find work here. “My goal is to find work for a better future for my daughters,” she said. Her husband, David Martinez, said they were tired but had to push on to reach their goal of making it to the U.S.

Olivin Castellanos, 58, a truck driver and mason from Villanueva, Honduras, said he took a raft across the river after Mexico blocked the bridge. “No one will stop us, only God,” he said. “We knocked down the door, and we continue walking.” He wants to reach the U.S. to work. “I can do this,” he said, pointing to the asphalt under his feet. “I’ve made highways.”

The migrants, who said they gave up trying to enter Mexico legally because the asylum application process was too slow and most want to continue to the U.S., gathered Saturday at a park in the border city of Ciudad Hidalgo. They voted by a show of hands to continue north en masse, then marched to the bridge crossing the Suchiate River and urged those still on it to come join them.

The decision to re-form the migrant caravan capped a day in which Mexican authorities again refused mass entry to migrants on the bridge, instead accepting small groups for asylum processing and giving out 45-day visitor permits to some. Authorities handed out numbers for people to be processed in a strategy seen before at U.S. border posts when dealing with large numbers of migrants.

But many became impatient and circumvented the border gate, crossing the river on rafts, by swimming or by wading in full view of the hundreds of Mexican police manning the blockade on the bridge. Some paid locals the equivalent of $1.25 to ferry them across the muddy waters. They were not detained on reaching the Mexican bank.

Sairy Bueso, a 24-year old Honduran mother of two, was another migrant who abandoned the bridge and crossed into Mexico via the river. She clutched her 2-year-old daughter Dayani, who recently underwent a heart operation, as she got off a raft.

“The girl suffered greatly because of all the people crowded” on the bridge, Bueso said. “There are risks that we must take for the good of our children.”

In addition to those who crossed the river, migrants were processed in small groups by immigration agents and then bused to an open-air, metal-roof fairground in Tapachula, where the Red Cross set up small blue tents on the concrete floor.

Migrants 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. The caravan elicited a series of angry tweets and warnings from President Donald Trump early in the week, but Mexico’s initial handling of the migrants at its southern border seemed to have satisfied him more recently.

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