Trump tweeted that he wanted "Mexico to stop this onslaught".
"One way or another, the way Mexico treats the undocumented immigrants from Central America affects Mexico's position in how it can criticize the US government for its treatment of undocumented Mexican immigrants in the United States", Salazar told CNN en Español.
The exhausted travelers are mostly from Honduras, but migrants from other Central American countries have joined the caravan.
A deal emerged Thursday night between the United States and Mexico to avert an approaching crisis triggered by the second caravan of illegal immigrants of 2018 heading toward the United States.
As the sun rose, a military helicopter could be seen overhead, foreshadowing the difficulties that migrants will have as they try to reach the U.S.
Trump has made security on the southern border one of the signature issues of his two-year presidency, calling for a "wall" and frequently railing against what he describes as a flood of rapists, gangs and "bad hombres".
Corzo said police accused Mujica of slashing the tires of an immigration vehicle.
Mexico's foreign ministry did not immediately respond to a request for comment.
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.
On Friday, Pompeo will meet officials including outgoing President Enrique Pena Nieto, foreign minister Luis Videgaray and Marcelo Ebrard, the designated foreign minister of Mexican President-elect Andres Manuel Lopez Obrador.
NBC reports that USA officials are now tracking that small group as they make progress towards the US.
Marcelo Ebrard, Lopez Obrador's pick to become foreign relations secretary after he takes office, said Trump's tweets needed to be understood in the context of the upcoming USA midterm elections.
He said he had spoken with Honduran President Juan Orlando Hernandez about ensuring the migrants who want to return home can do so safely.
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. Earlier this year, some National Guard members were deployed to the border on a limited mission that does not include contact with migrants.
"Only God on high can stop us", Escobar said.
Mauro Verzzeletti, a priest who runs the Casa del Migrante shelter in the Guatemalan capital, said about 3,000 people slept there overnight and left around 4 a.m.to continue the journey, adding that "more are arriving".
"In other words before they make the trek across Mexico?"