It's a push to show the country will make good on a deal to avoid USA tariffs.
Despite the president's insistence that there is a secret deal, the Mexican government has denied that there are any undisclosed parts of the U.S. - Mexico deal.
President Trump said it took two days to get what he wanted from Mexico thanks to the tariff threat.
Trump complained about France charging tariffs on USA wine in the past, tweeting in November that it's too hard for American wine producers to sell in France but the United States makes it "easy" to import French wines.
"We would start conversations about what they would like, which is for Mexico to become a safe third country", Ebrard said on a Mexican radio programme.
Under the deal, Mexico agreed to bolster security on its southern border and expand its policy of taking back asylum-seekers as the United States processes their claims.
"We have fully signed and documented another very important part of the Immigration and Security deal with Mexico, one that the USA has been asking about getting for many years". Mexico also pledged to reinforce its southern border with Guatemala with 6,000 members of its National Guard militarized police. They said they're fleeing poverty and violence in Honduras and the U.S.is still their destination regardless of Mexico's plans.
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"We have a fixed time period to prove that it is possible to reduce migration through development, through social welfare - that the use of force is not the only option", Lopez Obrador told a press conference.
"This is the first time we've heard anything like this kind of number of law enforcement being deployed in Mexico to address migration, not just at the southern border but also on the transportation routes to the northern border and in coordinated patrols in key areas along our southwest border", McAleenan said on "Fox News Sunday", adding that "people can disagree with the tactics", but "Mexico came to the table with real proposals". This avoids one of the biggest problems of our current policy, which allows asylum-seekers into the country, never to be removed, even if their claims are rejected and they are ordered deported.
The governments of Brazil, Panama and Guatemala did not immediately reply to requests for comment. Cuccinelli, a former attorney general of Virginia, has developed a reputation as a hardliner on immigration.
Mexico had no specific target for the reduction of migrant numbers, Ebrard said.
Ebrard said he thought Trump might be making a calculation based on Mexican agricultural imports when freed from the threat of tariffs. Mr Trump added American winemakers had complained to him that French wine can be imported into the United States "for nothing", but they have to pay steep duties to export their wine into France.
"The New York Times wrote a story like I already made the deal, it's nonsense, we talked about it for months and months and they wouldn't get there and we just said, hey look if you don't get there we're just going to have to charge you hundreds of billions of dollars in taxes", Trump said.