Thousands of Central American migrants engaged in a desperate move to reach the United States remained stranded Saturday on Mexico's southern border, but many remained unshakeable.

Migrants, who claim to escape poverty, poor working conditions and violence, slept all night on a bridge over the Suchiate River, without water or food, and without toilets, said eyewitnesses.

Some members of the caravan – mostly from Honduras – crossed the border with Guatemala on Friday and clashed with a wall of Mexican and Guatemalan peacekeepers who released pepper spray, forcing migrants to retire on the bridge.

On Saturday, the caravan organizers were moving people about 30 feet from the border gate to avoid a new run on the way and to establish a buffer zone with security guards.

Migrants have vowed to continue.

Jose Yanez, a 25-year-old farmer who claimed to earn about $ 6 a day, woke up early with back pain after a cold night on the bridge. "From there, we continue. From there, no turning back, "he said.

The group was in its infancy after a 1,100-kilometer trip to the US border. President Donald Trump has made a strong case for his immigration policy at rallies leading to the mid-term elections.

Trump raised the issue in a Saturday morning tweet derogating from the Democrats, saying that an immigration solution was still possible: "If the Democrats ceased to be obstructionists and met, we could draft and pass new immigration laws in less than an hour, look at the unnecessary pain and suffering they cause, look at the horrors unfolding at the border. "

Trump threatened to cut aid to Central America and close the southern border with Mexico if their respective governments failed to cope with the situation.

On Friday, women with young children stood en masse at the border gate, begging the Mexican police to let them pass.

"Please … let us go," pleaded Alba Luz Giron Ramirez, a former shop assistant and mother of three. She said her family had come from San Pedro Sula, Honduras, and that gangs had killed her brother and threatened him.

"We want them to give us permission to go to Mexico," said his 5-year-old son Ramon, in a low voice. "We would not stay."

Alison Danisa cried while she was kneeling in a garbage bin piling on the deck, squeezing her naked baby for 11 months against her chest. "We have suffered so much. She has a fever and we have not brought anything.

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Mexican President Enrique Pena Nieto said in a speech to the nation late Friday night that a large group of migrants had "tried to enter the Mexican territory in an irregular manner, attacking and even wounding some elements of the federal police ".

"Mexico does not allow and will not allow entry into its territory irregularly, let alone violently," he said.

Honduran President Juan Orlando Hernandez also tweeted Friday night to have met with his Guatemalan counterpart, Jimmy Morales, and to request permission to send Honduran civil protection personnel to the bridge for help migrants.

Selvin Flores, a 35-year-old trader from the Honduran city of Nacaome, said people who "caused trouble" were expelled from the group and turned over to the Guatemalan police.

Flores said he was skipping meals so that his three children could eat and hoped to earn money in the United States before returning to Honduras. Migrants, he said, "do not want misunderstandings."

Contributor: David Agren, United States TODAY & # 39; HUI; The Associated Press

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