"Full efforts are being made to stop the onslaught of illegal aliens from crossing our [southern] border", he tweeted.
Numerous migrants, the overwhelming majority fleeing violence and poverty in Honduras, slept on the bridge through heavy rain overnight, dozens of them crammed against a metal border gate guarded by Mexican police.
The caravan left San Pedro Sula in northern Honduras last week, following a call on social networks relayed by a former Honduran deputy. 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.
Aerial images show dense crowds at the Guatemala-Mexico worldwide bridge in Tecun Uman, Guatemala.
"They're not coming into this country", Trump said at the rally.
As the migrants continued their northward march about 900 miles from the US border, Trump tweeted that, "Sadly, it looks like Mexico's Police and Military are unable to stop the Caravan".
He went on to tweet that illegal immigration in the United States is due to Democrats "not giving us the votes to change our pathetic immigration laws!" "Change the immigration laws NOW!"
Migration is just as controversial in Mexico, where President-elect Andres Manuel Lopez Obrador said he will ask Mr. Trump to pony up more money to try to build Central American society and create jobs in Mexico, hoping to stem the flow of people to the U.S.
Some migrants were taken to a local fairground that had been converted into a temporary government shelter. "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".
Keeping together for strength and safety in numbers, some huddled under a metal roof in the city's main plaza Sunday night.
The group had exploded in size from the 2,000 people who had stopped overnight on Saturday.
Mr. Hernandez noted that migrants from elsewhere in the region had joined the caravan, along with others from "outside the region", though he did not cite specific nationalities.
Now in the thousands, the migrant caravan headed to the United States is still waiting to enter at City Hidalgo, Chiapas. They walked in a line stretching about a mile.
Cruz was among the many who appeared willing to accept any kind of migratory relief Mexico might offer.
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"One can not live back there", Vasquez said, standing next to the main border gate.
Passing freight trucks were quickly boarded by dozens of migrants, and straining tuk-tuks carried as many as a half-dozen.
Some camped on the bridge "are very aggressive and no longer have patience, they are already desperate because the Mexicans did not open the door to us", said Gina Paola Montes, 21, a humanities student from Honduras university.
Federal police monitored the caravan's progress from a helicopter and had a few units escorting it.
An unidentified police officer told Reuters there were no orders to block the caravan. On the Mexican side of the bridge, they were met by Mexican police in riot gear.
Maria Teresa Orellana, a resident of the neighbourhood of Lorenzo handed out free sandals to the migrants as they passed.
"One of my companions went to look for some plastic", she said. "They've really stepped up, and it will not be forgotten".
President Trump has threatened to call up the U.S. military and shut the border with Mexico to keep out the group.
Most of the people now caught trying to enter the United States illegally hail from Honduras, El Salvador and Guatemala, among the poorest and most violent countries in the Americas.
Approximately 640 migrants requested asylum in Mexico, according to a statement from the Mexican government and the National Migration Institute.
The migrant caravan is now in Guatemala, in the border town Tecún Umán, though some in the group have already crossed into Mexico. Mexican police tried to stop the human wave but after scuffling at a border crossing with Guatemala, Mexican police basically gave up.
The throng of Central American migrants marching toward the U.S. border has swollen to more than 5,000, despite Mexican efforts to stop them.
"We're warriors, we got to get to the place we got to get to". "We're going to figure it out", he said, suggesting his administration has a solution but planned to keep that information "low key until the election".
In another tweet, he said the migrants would not be allowed into the United States. Both leaders had spoken by phone with Pena Nieto and U.S. Vice President Mike Pence to discuss humanitarian aid and efforts to help people who want to return.