On Monday night, the Mexican government said it had stopped the caravan.
The move comes after Trump Sunday threatened to cut off immigration programs like DACA, as he targeted the refugee caravan with almost 1,350 migrants who were en route to Mexico and the United States on an arduous journey from the city of Tapachula in the state of Chiapas on the Mexico-Guatemala border, to demand an end to the political corruption in their cities, and dignity and the right to asylum from Mexico and the United States.
The organization that President Donald Trump called out on Twitter has given an equally scathing response.
A caravan of Central American migrants traveling through Mexico was stopped after its push to the U.S. border set off a barrage of criticism from U.S. President Donald Trump.
This may partially explain why, even after INM's announcement, caravan organizers from the pro-illegal immigration activist group Pueblo Sin Fronteras (PSF, "People Without Borders) have declared that the agency's decision is a victory for their group".
Mexico, however, does routinely stop and deport Central Americans, sometimes in numbers that rival those of the United States. "They must stop them at their Northern Border, which they can do because their border laws work, not allow them to pass through into our country, which has no effective border laws".
On Tuesday, Trump threatened that the "caravan" "had better be stopped before it" reached the USA border. He said the group did not expect to reach the US border for three more weeks.
The Central Americans now attempting to traverse Mexico mostly stream out of Guatemala, Honduras and El Salvador, where gang violence is rife and the murder rates have ranked among the highest in the hemisphere.
Members of the caravan who receive such visas will be able to travel unhindered by Mexico's police and other immigration enforcement agents. They must stop the big drug and people flows, or I will stop their cash cow, NAFTA.
The Mexican government said on Monday it had already sent back around 400 marchers to their home countries - an organizer said Sunday there were at least 1,200 Central American participants, largely from Honduras - "with strict adherence to the legal framework and full respect for their human rights".
"We will act with complete sovereignty in enforcing our laws", he said Monday.
"They have good intentions, but they're exposing (the migrants)" to danger, including trips on "La Bestia", a freight train that migrants steal rides on, said Jorge Andrade, spokesman for a coalition of mostly Catholic-run shelters known as the "You Are Us Collective".
It deported roughly twice as many Central Americans as the USA did in 2015 and 2016, according to Mexican and American government figures compiled by the Migration Policy Institute. The remaining migrants will be subjected to an "administrative migration procedure", the government said, though it was unclear how many marchers would be allowed to continue their journey to the US border. Trump has threatened to end NAFTA negotiations and pull out of the deal over the Mexican government's conduct.
Mexico has preferred to keep other issues such as security and immigration out of the NAFTA renegotiations, "unlike Trump. who puts everything on the table", said Brenda Estefan a former security attaché at the Mexican Embassy in Washington.