Pena Nieto added, addressing Trump, "if your recent statements are derived from your frustration with (U.S.) domestic politics, with your laws or your congress, deal with them, not with us Mexicans".
Besides ordering thousands of National Guardsmen to secure the border, the Republican president also threatened to ax what he called Mexico's "cash cow", the North American Free Trade Agreement (NAFTA), if the Mexican authorities did not stop the migrants.
Buzzfeed News, which first reported the caravan's movements last week, reported on Tuesday that organizers said the caravan would travel to Mexico City, where only those with valid asylum claims in Mexico or the USA would continue moving north to the border.
The Pentagon could not say where the money would come from and Trump admitted the White House was still "looking at" costs.
"This great threat on the southern border of the United States that he says is there, does not exist", said the leftist Lopez Obrador, who has a double-digit lead in most polls.
The front-runner in the race, Andres Manuel Lopez Obrador, said Trump's scheme was political "propaganda" based on misinformation that aimed to stir up "xenophobia" and "racism".
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"This anti-Mexican policy has worked politically because unfortunately there are conservative sectors in the United States with little information and he knows how to awaken an anti-Mexican sentiment", he added during a campaign event in the northern border city of Nuevo Laredo.
"The presidential candidates, independently of their natural differences, all of them coincided in rejecting these measures that run counter to good relations between neighbors", Pena Nieto said in a broadcast message.
Peña Nieto told Trump that if he is unhappy with immigration trends in the United States, he should take the issue up with Congress, and not lash out at Mexico. "We must make it clear to President Trump that Mexico and the United States can continue to have a profitable relationship, of mutual benefit, or move into a confrontational relationship, where we all lose", Anaya said.
Presidential candidate Jose Antonio Meade, backed by the Institutional Revolutionary, Green and New Alliance parties, considered Trump's plans to send soldiers to the borderline an "inadmissible grievance".
"As president of all Mexicans, I agree with (their) remarks", he said.