Trump has called the 'caravan' a US 'national emergency', alerted the US Border Patrol and military, and said he will begin cutting off aid to Guatemala, Honduras and El Salvador.
A US-bound caravan of thousands of mostly Honduran migrants whom President Donald Trump has declared unwelcome, crowded into the Mexican border city of Tapachula on Sunday, setting up impromptu camps in public spaces under a heavy rain.
(Text inputs from Reuters)
Members of the caravan, exhausted from the hours-long trek on foot from the Guatemalan border, mostly ignored police offers to board buses heading to a migrant shelter because of suspicions they might be deported instead.
The migrants have defied threats by Trump that he will close the US-Mexico border if the caravan advances, as well as warnings from the Mexican government that they risk deportation if they cannot justify seeking asylum in Mexico.
A large column of people marched under a burning sun Sunday as a military helicopter circled low overhead.
Many migrants said they were fleeing a toxic mix of violence, poverty and corruption in Central America.
Most said they felt safer advancing in a large group.
Mexican President-elect Andres Manuel Lopez Obrador supported the caravan and promised to provide people with work permits in a speech to supporters in Tuxtla-Gutierrez, about 180 miles (290 km) north of Tapachula.
"I want to tell them they can count on us," said Lopez Obrador, who will take office in December, to a smattering of applause.
He reiterated that is seeking Trump's support to help fund a development plan that could alleviate poverty in Central America and southern Mexico.
Trump said Monday that he is cutting off aid to Guatemala, Honduras and El Salvador. He has also said he will send his army to the border to stop the 'caravan', made up largely of migrants from Honduras.
Mexico's government has said throughout the past week that it would register the migrants and process requests for asylum.
Those attempting to skip the process would face deportation, but the size of the caravan will test Mexico, which has sought help from the United Nations to manage the issue.