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Thousands of Central American migrants hoping to reach the U.S. were deciding Monday whether to rest in this southern Mexico town or resume their arduous walk through Mexico as President Donald Trump rained more threats on their governments.

After blaming the Democrats for "weak laws" on immigration a few days earlier, Trump said via Twitter Monday: "Every time you see a Caravan, or people illegally coming, or attempting to come, into our Country illegally, think of and blame the Democrats for not giving us the votes to change our pathetic Immigration Laws!" He apparently sees the caravan as a winning issue for Republicans a little over two weeks ahead of midterm elections.

In another tweet, he blamed Guatemala, Honduras and El Salvador for not stopping people from leaving their countries. "We will now begin cutting off, or substantially reducing, the massive foreign aid routinely given to them," he wrote.

A team of AP journalists traveling with the caravan for more than a week has spoken with Hondurans, Guatemalans and Salvadorans, but has not met any Middle Easterners of the sort Trump suggested were "mixed in" with the Central American migrants.

It was clear though that more migrants were continuing to join the caravan.

José Anibal Rivera, 52, an unemployed security guard from San Pedro Sula crossed into Mexico by raft Sunday and walked up to Tapachula from Ciudad Hidalgo to join the caravan. "There are like 500 more people behind me," he said.

He vowed to reach the U.S. border, still nearly 2,000 road miles away at its closest point. "Anything that happens, even if they kill me, is better than going back to Honduras," he said.

Ana Luisa España, a clothes washer and ironer from Chiquimula, Guatemala, joined the caravan as she saw it pass through Guatemala.

'The goal is to reach the (U.S.) border," she said. "We only want to work and if a job turns up in Mexico, I would do it. We would do anything, except bad things."

Isis Ramirez, 32, a mother of three from Tegucigalpa, Honduras, awoke Monday morning on a square of sodden cardboard in Tapachula's town square, her swollen feet stretched out in front of her, wrapped in bandages applied by paramedics. Blisters had formed on her feet from the cheap plastic sandals she wears.

"There are more sick people. It's better that we rest today," she said.

Nearby, Julio Asturias, 27, a migrant from San Juan, El Salvador charged his cellphone from a dangling wire.

"I want to return to Arizona, and when I heard that the caravan was passing, I joined it," he said. He said he was deported a couple of months ago after police pulled him over for a burned-out tail light.

On Sunday thousands of migrants stretched out on rain-soaked sidewalks, benches and public plazas in Tapachula, worn down by another day's march under a blazing sun.

Keeping together for strength and safety in numbers, some huddled under a metal roof in the city's main plaza Sunday night. Others lay exhausted in the open air, with only thin sheets of plastic to protect them from ground soggy from an intense evening shower. Some didn't even have a bit of plastic yet.

"We are going to sleep here in the street, because we have nothing else," said Jose Mejia, 42, a father of four from the Honduran city of San Pedro Sula. "We have to sleep on the sidewalk, and tomorrow wake up and keep walking. We'll get a piece of plastic to cover ourselves if it rains again."

Mexican President-elect Andres Manuel Lopez Obrador suggested Sunday that the United States, Canada and Mexico work out a joint plan for funding development in the poor areas of Central America and southern Mexico.

"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.

The migrant caravan, which started out more than a week ago with fewer than 200 participants, has drawn additional people along the way and it swelled to an estimated 5,000 Sunday after many migrants found ways to cross from Guatemala into southern Mexico as police blocked the official crossing point.

Later in the day, authorities in Guatemala said another group of about 1,000 migrants had entered that country from Honduras.

In interviews along the journey, migrants 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.

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

Civil defense officials for Mexico's southern state of Chiapas said they had offered to take the migrants by bus to a shelter set up by immigration officials about 5 miles (7 kilometers) outside Tapachula, but the migrants refused, fearing that once they boarded the buses they would be deported.

Ulises Garcia, a Red Cross official, said some migrants with injuries from their hard trek refused to be taken to clinics or hospitals, because they didn't want to leave the caravan.

"We have had people who have ankle or shoulder injuries, from falls during the trip, and even though we have offered to take them somewhere where they can get better care, they have refused, because they fear they'll be detained and deported," Garcia said. "They want to continue on their way."

Garcia said he had seen cases of swollen, lacerated and infected feet. But "they are going to continue walking, and their feet won't heel as long as they keep walking," he said.

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."