An official from Mexico's National Institute of Migration said Mexico plans to disperse the caravan by Wednesday, but some people such as pregnant women or those with disabilities would get humanitarian visas.
The White House on Tuesday said mobilizing the National Guard was part of Trump's strategy to stop illegal immigrants from entering the country, whom he blames for crime and drug trafficking.
Trump's comments this week directed at Mexico have thrust the countries' relationship into the centre of Mexico's presidential campaign, where the ruling party is trailing.
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And before Trump credited Mexico's "strong immigration laws" for dispersing much of the migrant group on Thursday, earlier this week he warned that he would "stop their cash cow, NAFTA", if the country doesn't reduce the flow of immigrants coming across the southern USA border.
Leaders of the organization behind the caravan, People Without Borders, said the procession of people would end in Mexico City rather than attempt to reach the border. Although his administration has at times cited a "Trump effect" for what it said was a dip in border crossings, the number of migrants trying to illegally cross into the US at the Mexico border spiked dramatically in March, according to figures released by US Customs and Border Protection.
But that didn't sit well with some Mexican political forces.
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Ricardo Anaya, the second-place candidate who heads a right-left coalition, backed the Senate motion at a news conference early on Thursday.
Independent candidate Margarita Zavala, trailing in fourth place in recent polls, on Thursday called Trump's announcement a "historic error" that would hurt the United States as much as Mexico.
Pena Nieto has twice canceled plans to visit Washington after tense phone calls with Trump in which the Republican president refused to back down from his insistence that Mexico pay for his planned border wall.
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"We are convinced that, by coming to agreements as friends, partners and good neighbors, both countries will fare better than if we confront each other", Pena Nieto said. "I urge you to reconsider this hostile act".