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"The Caravan is largely broken up thanks to the strong immigration laws of Mexico and their willingness to use them so as not to cause a giant scene at our Border", the president tweeted.

Mexico's Senate on Wednesday called on the government to end cooperation with the United States on migration and security over Trump's plans to deploy the National Guard along their shared border.

As tensions between Mexico and the United States heat up over a migrant caravan reportedly seeking to cross the border, families forming part of the group have begun registering with Mexican immigration officials to safeguard their status in the country.

Trump adds that "Border crossings are at a still UNACCEPTABLE 46 year low".

The Mexican government denied they had been influenced by Trump's threats of cutting aid and his decision to send the National Guard to the border, and declared the Caravan had stopped by its own choice.

Lopez Obrador said crime rates in US border cities have been falling in recent years, as has the number of Mexicans seeking to cross the border.

"Homeland Security Secretary Kirstjen Nielsen said she had been working with governors of the southwest border states to develop agreements on where and how many Guardsmen will be deployed".

"Why not yesterday and tomorrow?"

The front-runner in Mexico's presidential race on Thursday said U.S. President Donald Trump's plan to send National Guard troops to the border was a political ploy based on misinformation to gain support from his conservative base.

Mexican senators have asked Mexican President Enrique Peña Nieto to "suspend the nation's cooperation with the United States on several issues" in response to President Trump's constant criticism and aggressiveness against the Central American country, The Hill reported.

In his tweets about the caravan earlier this week, Trump threatened to pull foreign aid from Honduras - where numerous caravan's participants are emigrating from.

An organizer of the volunteer group that organized the caravan, said that migrants would keep moving, but in smaller groups according to a report Tuesday.