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 approximately 1.5 kilometres.

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 travellers had materialized from since about 2,000 had been gathered on the Mexican side Saturday night. But people have been joining and leaving the caravan daily, some moving at their own pace and strung out in a series of columns as they moved across Guatemala.

They marched on through Mexico, shouting triumphant slogans like "Si se pudo!" or "Yes, we could!"

Watch: Migrants break Guatemala border fence

Mexican television footage shows hundreds of migrants pushing through Guatemalan border posts and streaming onto a bridge connecting Mexico and Guatemala. 1:35

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 neighbourhood 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 favourite — and only — toy of her two daughters, Victoria 4 and Elisabeth, 3, as they trudged beside her, all covered in sweat.

A business administration graduate, Lopez said she couldn't find work in Honduras. She wants to reach the U.S. 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."

Caravan re-formed in Mexico

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 circumventing 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 US to ferry them across the muddy waters. They were not detained on reaching the Mexican bank.

Although several hundred applied for refugee status in Mexico, a growing number of migrants resumed their advance toward the U.S. border on Sunday. (Adrees Latif/Reuters)

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 had recently had 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, immigration agents processed migrants in small groups and then bused them to an open-air, metal-roof fairground in Tapachula, where the Red Cross set up small blue tents on the concrete floor.

Mexico's Interior Department said 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.

Watch: See the migrant caravan from above

CNN captured footage of migrants gathered on a bridge, as some jumped into the river below. 0:38

On Sunday, Mexican federal police monitored the caravan's progress from a helicopter and had a few units escorting it. Outside Tapachula about 500 federal police briefly gathered along the highway on buses and in patrol units, but officers said their instructions were to maintain traffic on the highway not stop the caravan. They moved on toward Tapachula before the caravan reached them.

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.

Juan Carlos Mercado, 20, from Santa Barbara, Honduras, says corruption and a lack of jobs in Honduras has stymied him. "We just want to move ahead with our lives," he said Sunday. He said he'd do any kind of work.

Trump blames Democrats

Trump again hammered the Democratic Party over the mass caravan of migrants.

Trump has seized on the caravan and border security in general as a campaign issued ahead of midterm elections in early November, and on Sunday afternoon he let loose anew.

The president tweeted: "The Caravans are a disgrace to the Democrat Party. Change the immigration laws NOW!"

In a separate tweet, he said that: "Full efforts are being made to stop the onslaught of illegal aliens from crossing our Souther Border."

Trump added that the United States will turn migrants away if they do not apply for asylum first in Mexico.