President Trump, seizing on what he sees as a vote-winning issue as the mid-term elections approach, has threatened to shut off all access to the United States, using military force if necessary.
Earlier in the week, the United States president had threatened to cut aid to Honduras and send United States troops to the Mexican border.
Developing story - more to come.
Hondurans have the right to free movement in some Central American countries, although there have been reports of migrants being blocked at the Guatemalan border.
Hundreds of Mexican police officers and troops have stationed themselves along the other side of the tall fence which separates it from Guatemala.
If Trump pulls out of the trade deal or closes the border, there would be major economic implications for both countries.
Mexico has rushed to contain the situation. One administration, that of President Enrique Peña Nieto, is leaving office and the new one, of President-elect Andres Manuel Lopez Obrador, isn't yet through the door.
The migrants have agreed that they will begin their journey to the border crossing between Guatemala and Mexico around 11 a.m. local time.
Why does it concern Trump?
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They blame the Trump administration for backing the Honduran government, and accuse the U.S. president of scapegoating migrants and refugees.
Where is the caravan now?
He called on Mexico to ensure the migrants do not reach the USA border while threatening Guatemala, Honduras and El Salvador with financial penalties.
The latest focus is on more than 2,000 Hondurans who left last Saturday from the city of San Pedro Sula.
The migrants are mostly Hondurans, but others like Salvadoran Jonathan Guzman have joined the caravan en route.
"This caravan did not appear organically", a senior Trump administration official told journalists.
"Mexico also issued a very clear statement saying if somebody is seeking asylum, Mexico is there along now with the U.N.to look at those claims, we want to make sure those claims are legitimate".
And according to worldwide law, the United States can not deport asylum seekers without first determining the validity of their claim.
CNN's Bill Weir was on a bridge that links Mexico and Guatemala Friday, as the caravan of migrants pushed through the border. "Now we're being pushed back", Weir said.
Secretary of State Mike Pompeo met with his Mexican counterpart, Foreign Minister Luis Videgaray, on Friday in an attempt to negotiate a plan on dealing with the large group.
Image copyright Getty Images Image caption The group was held at the border by Guatemalan police on Monday for several hours What will happen to the people?