Here are five things to know about the men and women, mostly from Central America, waiting for Mexico to decide their fate.
Migrant rights groups are distancing themselves from a caravan of roughly 1,200 Central Americans claiming that its size and sheer force north could bring about a plethora of problems for future migrants.
Mexico is doing very little, if not NOTHING, at stopping people from flowing into Mexico through their Southern Border, and then into the U.S. They laugh at our dumb immigration laws.
The caravan is in fact a yearly event held since 2010.
"But since we're refugees, they should treat us like refugees", Mujica said to the crowd.
"The big Caravan of People from Honduras, now coming across Mexico and heading to our "Weak Laws" Border, had better be stopped before it gets there".
"Donald Trump wanted the world to crush us, to erase our existence".
"We have support teams at the border if there are people who need assistance there, but they would have to travel on their own", he told AFP in the town of Matias Romero, in the southern Mexican state of Oaxaca.
No, Trump doesn't really want to bomb the caravan. Cash cow NAFTA is in play, as is foreign aid to Honduras and the countries that allow this to happen.
"Our dream is to build solidarity bridges among peoples and turndown border walls imposed by greed", they said.
"That they open the borders to us because we are as much citizens as the people of the countries where we are and/or travel". Migrants take shade under tarps or scrawny palms. She was breast-feeding her eight-month-old son, Brian, inside a chaotic room where officials registered migrants.
A caravan of Central American migrants whose trek across Mexico infuriated Donald Trump on Wednesday scrapped plans to cross into the United States, as the American president ordered the National Guard to deploy to the border.
"The Mexican government has proceeded when appropriate with repatriations". On Tuesday, Mexican immigration officials began taking a census at the migrant encampment.
On Monday, Mexican immigration officials began taking the names of people interested in filing for asylum, or temporary transit or humanitarian visas in Mexico. They flow through Mexico. Many say they never intended on going all the way to the United States after the end of the "Stations of the Cross" caravan.
A handful of migrants with strong claims for asylum will continue to the USA border on their own, he said. "Under no circumstances does the Mexican government promote irregular migration", the Interior Ministry statement said.
The Trump administration's announcement was also condemned by the front-runner to win the Mexican presidency in a July 1 election, leftist Andres Manuel Lopez Obrador.
Mexico's chief technical negotiator on the trade deal, Kenneth Smith Ramos, tweeted Tuesday that the country "will continue working in a constructive manner" in the NAFTA negotiations.
She would like to get into the USA, where she has a cousin in Houston.
Central American migrants receive donated clothes as they take a break from traveling in their caravan, on their journey to the US, in Matias Romero, Oaxaca, Mexico, April 3, 2018.
"I see it as something really sad, because I don't understand how a child this age can make things hard for him", said Hernandez, a 27-year-old who is two months pregnant.
The movement was organized by a called group Pueblo sin Frontera with the slogan "We are all Native Americans".
Trump again sounded the "caravan" alarm, but he did so in a tweet whose syntax seemed to wander as it pivoted from earlier complaints over conditions in Mexico to blaming problems in the US for the situation.
"Sending US service members to patrol the US-Mexico border is wrong", tweeted Representative Beto O'Rourke, who represents the border city of El Paso and is running for the US Senate against Republican Senator Ted Cruz.