Even the recently renegotiated North America Free Trade Agreement (NAFTA) between Mexico, the United States and Canada, which is now known as USMCA, could be under threat, Trump said.
The move came after President Donald Trump threatened to use military force to completely close the US-Mexico border over the issue.
Changes to detention rules saw thousands of migrant children detained and separated from their parents earlier this year, sparking national and worldwide condemnation.
But in Mexico, where protesters alreadyhave been marching in support of the approaching Honduran migrants, caving to US pressure wouldn't play almost as well.
"One way or another, we will pass", they changed, clambering atop to USA -donated military jeeps parked at the scene as Guatemalan police looked on.
Central American migrants hiked from Honduras through muddy jungle and residential streets, some toting babies along with backpacks, Reuters images show.
In a speech Thursday night, Trump accused the Democrats of paving the way for the caravan with their sanctuary city policies.
One Honduran human rights group said the migration was more a case of "forced displacement" than voluntary emigration, although the Honduran government has warned people not to join an "irregular movement" it describes as "political".
"It's a very hard situation for the Mexican government", says Ana Maria Salazar, a former Pentagon official who's now a security analyst in Mexico City.
The migrants planned to wait for the rest of the caravan to arrive, then cross the border en masse in hopes of overwhelming the Mexican authorities, who have vowed to detain anyone without a visa.
"(Criminals) have infrastructure that is built up already and are put into place inside the caravans", he said.
The migrants are fleeing their country because of violence and poverty.
Though it began with just a couple hundred Hondurans headed for the United States, the support flowing in from leftist organizers and funders has grown this new caravan of hopeful immigrants into the thousands.
Mexican authorities have also said they're asking for help from the United Nations High Commissioner for Refugees to process migrants seeking refugee status at the country's southern border.
Honduran migrants, part of a caravan trying to reach the USA, line up to enter a migrant shelter in Guatemala City, Guatemala October 17, 2018.
"Honestly, I want to get to the states to contribute to that country, to do any kind of work, picking up garbage", he said.
It also was not clear Thursday if the military could legally be used to shut down the U.S. -Mexico border.
On Thursday, Trump referred to the caravan as an "assault on our country", citing "criminal elements and drugs pouring in".