ESQUIPULAS, GUATEMALA—U.S. President Donald Trump threatened Tuesday to cut aid to Honduras if it doesn’t stop a caravan of some 2,000 migrants, even as they resumed their northward trek through Guatemala with hopes of reaching the U.S. border.

Despite having walked the entire previous day, with swollen, blistered and aching feet, the group was up shortly after sunrise after sleeping on the ground in their clothes.

Dozens attended Mass at the Basilica in the city of Esquipulas, just across the border from Honduras and about 90 miles (150 kilometres) east of Guatemala City, to receive a blessing, before continuing the journey escorted by Guatemalan police.

The group’s numbers have snowballed since some 160 migrants departed Friday from San Pedro Sula, Honduras, with many people joining spontaneously carrying just a few belongings. A Guatemalan priest estimated that more than 2,000 had been fed at three shelters run by the Roman Catholic Church.

Three weeks before midterm elections in the United States, the caravan elicited a tough response from Trump.

“The United States has strongly informed the President of Honduras that if the large Caravan of people heading to the U.S. is not stopped and brought back to Honduras, no more money or aid will be given to Honduras, effective immediately,” Trump tweeted.

However, the Central American nation’s ability to do anything at this point appeared limited as the migrants had already crossed into Guatemala on Monday, twice pushing past outnumbered police sent to stop them — first at the border and then at a roadblock outside Esquipulas.

Trump did not follow through on a similar threat to the Central American nation in April over an earlier caravan, which eventually petered out.

There was no immediate public response from the Honduran government. In late September, in a speech at the U.N. General Assembly, President Juan Orlando Hernandez defended migrants, criticizing their treatment in detention centres and the separation of children from their families — without explicitly naming the United States.

“Migration is a human right,” Hernandez said. “For centuries human beings have moved and emigrated and have contributed to the social and economic development of the nations that have taken them in, in search of better opportunities. We in Honduras and the Central American region are not an exception.”

Meanwhile, Mexico’s immigration authority sent out a fresh warning late Monday that only those who meet entry requirements would be allowed into the country and each migrant would have to satisfy Mexican migration agents. Hondurans need visas to visit Mexico in most cases.

Still, it remains unclear if Mexico and other governments in the region — many of whose own people are migrants — would have the political will to physically halt the determined border-crossers, who are fleeing widespread poverty and violence in one of the world’s most murderous countries.

“In Honduras there are no jobs, and the jobs that do exist aren’t enough to live on,” said Jose Francisco Hernandez, a 32-year-old from Copan state in western Honduras. “We can’t go to the city because it is full of gang members, and that is hurting us. We decided to migrate from the country to see if we can find a better life.”

Carlos Reyes, 20, said he was attacked a week ago for being gay and dressing in women’s clothing.

“Some men were going to kill me. ... They wanted to kill me for who I am,” Reyes said.

The migrants hope that travelling en masse affords them protection from robbery, assault and other dangers that plague the journey north.

Many carried only a few belongings in backpacks and bottles of water. Some pushed strollers or carried toddlers on their shoulders.

On Monday night they bedded down wherever they could, some on the grass in a church parking lot and others on the floors of a migrant shelter and a sports hall.

Few carried food and some Esquipulas residents began to organize to help feed them. Some migrants asked for money, while others were handed bread as they passed a local bakery.

Last week, U.S. Vice-President Mike Pence urged leaders in Honduras, El Salvador and Guatemala to persuade their citizens to stay home and avoid the long, risky journey to the United States.

On Tuesday, Pence tweeted that he had spoken with Hernandez, the Honduran president.

“Delivered strong message from @POTUS: no more aid if caravan is not stopped. Told him U.S. will not tolerate this blatant disregard for our border & sovereignty.”

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But the threat of ending aid to an unpopular government seemed unlikely to dissuade the migrants, some of whom expressed displeasure with Hernandez.

Gabriela Natareno, 27, who was travelling with her 16-year-old cousin, said her president is to blame for continued migration by desperate Hondurans.

“He keeps the country mired in poverty and corruption,” she said.