US President Donald Trump has said the migrants would not be allowed into the United States, calling the caravans "a disgrace to the Democrat party."
Thousands of Honduran migrants hoping to reach the US stretched out on rain-soaked sidewalks, benches and public plazas in the southern Mexico city of 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."
Adela Echeverria, 52, a single mother of three, teared up as she spoke about her plight.
"One of my companions went to look for some plastic," she said. "We are used to sleeping like this, taking care of each other. We don't want to be separated."
The group's advance has drawn strong criticism from US President Donald Trump, who lashed out again on Sunday at the Democratic Party 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!"
Later on Monday, Trump said he had alerted border patrol and the military that the caravan is a national emergency.
"Sadly, it looks like Mexico's Police and Military are unable to stop the Caravan heading to the Southern Border of the United States. Criminals and unknown Middle Easterners are mixed in. I have alerted Border Patrol and Military that this is a National Emergy. Must change laws!" Trump tweeted.
In another tweet, he said the migrants would not be allowed into the United States.
Mexican President-elect Andres Manuel Lopez Obrador suggested Sunday that the United States, Canada and Mexico work out a join t 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.