'In addition to stopping all payments to these countries, which seem to have nearly no control over their population, I must, in the strongest of terms, ask Mexico to stop this onslaught - and if unable to do so I will call up the U.S. Military and CLOSE OUR SOUTHERN BORDER!' he wrote in one tweet.
Around 4,000 people have fled ongoing violence in Honduras, where "gangs exercise widespread control in certain neighborhoods", The New York Times reports.
In morning tweets, Trump repeated vows to stop US aid to Central American countries that do not disband the caravan and issued a fresh threat to the Mexican government, which said Wednesday that it would treat those in the caravan no differently than it does other migrants.
The developments on Friday came as Mike Pompeo prepared to fly to Mexico to discuss migration with the country's officials.
His successor, Andres Manuel Lopez Obrador, takes office December 1.
"In Mexico we have the rule of law, and we shall apply, enforce the law", Videgaray told reporters.
On Thursday he threatened to close the U.S. border if Mexico didn't stop the caravan.
In a series of tweets, Trump blamed Democrats, leaders of Central American countries and "existing weak laws" for the influx. Indeed, some have already reached Mexico and requested asylum.
A chaotic scene unfolded as a massive caravan of Honduran migrants reached the Guatemala-Mexico border Friday.
Migrant caravans of this type are nothing new, they quite often take place.
But foreign minister Videgaray said that was "false" and that no such deal had been made.
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The exhausted travelers are mostly from Honduras, but migrants from other Central American countries have joined the caravan.
Shortly afterwards, Guatemala's government tweeted that Mr Hernandez would meet Mr Morales today in Guatemala City to implement a strategy for returning the Honduran migrants. The nearest border is about 110 miles (177 km) away.
They plan to cross Mexico's border in the coming days, then continue north to the United States. He also suggested they are ready to welcome the migrants with open arms because they are likely to vote for them in elections.
"Mexico does not and will not allow (people) to enter its territory illegally, let alone violently", he said. Immigration officials said later in a statement that Mujica, who has dual U.S.
In an apparent attempt to rally his base, Trump, in his Twitter posts, has invoked the same kind of anti-immigrant fears he used during his 2016 campaign, warning of an "onslaught" of criminals.
Mexico's main reaction has been to step up security on its southern border with Guatemala. "The United States stands ready to assist the Government of Mexico and UNHCR in this effort".
The caravan formed Saturday in San Pedro Sula, Honduras.
He said he had spoken with Honduran President Juan Orlando Hernandez about ensuring the migrants who want to return home can do so safely.
Foreign Minister Luis Videgaray plans to make the formal request during a meeting Thursday with U.N. Secretary General Antonio Guterres in NY.
Guatemala also had troops at the border.