Central American migrants walking to the U.S. start their day departing Ciudad Hidalgo, Mexico, Sunday, Oct. 21, 2018. Despite Mexican efforts to stop them at the border, about 5,000 Central American migrants resumed their advance toward the U.S. border early Sunday in southern Mexico. (AP Photo/Moises Castillo)

Central American migrants walking to the U.S. start their day departing Ciudad Hidalgo, Mexico, Sunday, Oct. 21, 2018. Despite Mexican efforts to stop them at the border, about 5,000 Central American migrants resumed their advance toward the U.S. border early Sunday in southern Mexico. (AP Photo/Moises Castillo)

TAPACHULA, Mexico (AP) — A growing caravan of Honduran migrants streamed through southern Mexico on Sunday heading toward the United States, after making an end-run around Mexican agents who briefly blocked them at the Guatemalan border.

They received help at every turn from sympathetic Mexicans who offered food, water and clothing. Hundreds of locals driving pickups, vans and cargo trucks stopped to let them clamber aboard.

Besi Jaqueline Lopez of the Honduran city of San Pedro Sula carried a stuffed polar bear in a winter cap that seemed out of place in the tropical heat. It’s the favorite — and only — toy of her two daughters, 4-year-old Victoria and 3-year-old Elisabeth, who trudged beside her gleaming with sweat.

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A business administration graduate, Lopez said she couldn’t find work back home and hopes to reach the United States, but would stay in Mexico if she could find employment here.

“My goal is to find work for a better future for my daughters,” she said.

In dozens of interviews along the journey, they have said they are fleeing widespread violence, poverty and corruption in Honduras. The caravan is unlike previous mass migrations for its unprecedented large numbers, and because it largely began spontaneously through word of mouth.

Guatemala’s migration agency confirmed that another group of about 1,000 migrants crossed into the country from Honduras on Sunday.

After praising Mexico for its no-nonsense response when police at a southern border bridge pushed the migrants back with riot shields and pepper spray, U.S. President Donald Trump again hammered Democratic Party opponents over what he apparently sees as a winning issue for Republicans a little over two weeks ahead of midterm elections.

After blaming the Democrats for “weak laws” on immigration a few days earlier, Trump said via Twitter: “The Caravans are a disgrace to the Democrat party. Change the immigration laws NOW!”

“Full efforts are being made to stop the onslaught of illegal aliens from crossing our Souther (sic) Border,” he said in another tweet. “People have to apply for asylum in Mexico first, and if they fail to do that, the U.S. will turn them away. The courts are asking the U.S. to do things that are not doable!”

Hundreds of migrants from the caravan did just that — applied for refugee status in Mexico in the southern city of Ciudad Hidalgo. By Sunday evening, the Interior department reported that it had received more than 1,000 requests.

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But a far bigger group forded the Suchiate River from Guatemala to the Mexican side individually and dozens at a time, and resumed the trek at first light, marching 10 abreast on the highway.

“Si se pudo!” they chanted in Spanish — “Yes, we did!”

The throng grew even larger than when the migrants arrived at the border bridge, swelling overnight to 5,000.

It was not immediately clear where the additional travelers came 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.

Their destination Sunday was the city of Tapachula in Chiapas state. Under a blazing sun, small groups of 20 to 30 paused to rest in the shade of trees on the side of the road, and by afternoon the caravan had evolved into long lines of walkers straggling for miles.

Jesus Valdivia, of Tuxtla Chico, Mexico, was one of the many who pulled his pickup truck over to let 10 or even 20 migrants hop in at a time, sometimes causing vehicles’ springs to groan under the weight.

“You have to help the next person. Today it’s for them, tomorrow for us,” Valdivia said, adding that he was getting a valuable gift from those he helped: “From them we learn to value what they do not have.”

Passing freight trucks were quickly boarded by dozens of migrants, and straining tuk-tuks carried as many as a half-dozen.

Brenda Sanchez of San Pedro Sula, Honduras, who rode in Valdivia’s truck with three nephews ages 10, 11 and 19, expressed gratitude to “God and the Mexicans who have helped us.”

She even had kind words for Mexican police: “We are very grateful to them because even though they closed the doors to us (at the border), they are coming behind us taking care of us.”

Federal police monitored the caravan’s progress from a helicopter and had a few units escorting it. Outside Tapachula, about 500 black-uniformed officers briefly gathered along the highway on buses and in patrol units, but they said their orders were to maintain traffic and not to stop the caravan. They moved on toward the city before the caravan reached them.

As the migrants passed through villages on the outskirts of Ciudad Hidalgo, locals applauded, shouted encouragement and donated supplies.

Maria Teresa Orellana, a resident of Lorenzo, handed out sandals. “It’s solidarity,” she said. “They’re our brothers.”

Mexico’s Interior Department said in a statement that federal and Chiapas state authorities were providing assistance to migrants, including legal counseling for those who applied for asylum. It released a video showing workers doling out food, medicine and medical treatment.

In comments to reporters after a rally in Elko, Nevada, on Saturday night, Trump said of Mexico’s response: “I just want to say, on behalf of the American public, that we appreciate what Mexico is doing. They’ve really stepped up, and it will not be forgotten.”

Trump also repeated: “I will seal off the border before (the migrants) come into this country, and I’ll bring out our military, not our reserves.”

Mexican President-elect Andres Manuel Lopez Obrador said he was suggesting to Trump that the United States, Canada and Mexico seek an agreement to invest in development in Central America and southern Mexico, which is home to many of that country’s poor.

“In this way we confront the phenomenon of migration, because he who leaves his town does not leave for pleasure but out of necessity,” said Lopez Obrador, who takes office Dec. 1.

Mexican authorities had refused to allow the caravan mass entry from Guatemala, instead accepting small groups to process asylum requests and handing out some 45-day visitor permits. An estimated 1,500 were still on the Guatemalan side of the Suchiate, hoping to enter legally.

But police could do little if anything in the face of the throngs who avoided the official entry point and crossed the notoriously porous border elsewhere.

Migrants marching north Sunday said they gave up on Mexico because the application process was too slow, and most wanted to continue to the United States anyway.

“We’re warriors, we got to get to the place we got to get to. We’re gonna keep on going and we’re not gonna stop,” Luis Puerto, 39, of Colon, Honduras, said in English.

For Puerto, that place is North Carolina, where he has a wife and two daughters. He said he was recently deported from the United States after a brush with the law that he did not specify.

“We are going to get to the border of the U.S.,” he said. “I am not going to stop. I don’t care if I die.”

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Associated Press writers Sonia Perez D. in Tecun Uman, Guatemala, and Peter Orsi in Mexico City contributed to this report.