The MPP, which was enacted on January 24, forces asylum-seekers traveling north into the United States to wait in Mexico while their claims are processed.
Trump put the number of troops at 6,000, and said in a tweet Saturday, "Mexico will try very hard, and if they do that, this will be a very successful agreement for both the United States and Mexico!"
Mnuchin, who said he participated in a call with Trump just before the deal was announced, said the president would retain the right to impose tariffs if Mexico did not keep its commitments.
Mexico also agreed to take stronger measures to curb the flow of migrants, including deploying militarised National Guard forces on its southern border beginning on Monday.
A "US-Mexico Joint Declaration" released by the State Department says the US "will immediately expand the implementation" of a program that returns asylum-seekers who cross the southern border to Mexico while their claims are adjudicated.
"In the face of naysayers, President Trump yet again delivered a huge victory for the American people", Trump campaign spokesman Tim Murtaugh said in a statement, applauding the president for using "the threat of tariffs to bring Mexico to the table" and "showing that he is willing to use every tool in his toolbox to protect the American people".
The move takes direct aim at Mexico's economy, which is heavily dependent on trade with the United States.
Short hit back at the uneasy Republican lawmakers on Friday.
Pompeo is praising Mexican Foreign Minister Marcelo Ebrard after three days of negotiations. Mexico has rejected those offers in the past, but USA officials have said that Mexico was more open to some version of this idea in talks on Thursday.
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Which is, with out a doubt, very quite lots of than announcing "we want to initiate the impeachment inquiry now". Impeachment, the constitutional remedy for presidential wrongdoing, is how a president is removed from office.
Treasury Secretary Steven Mnuchin hailed the deal between the U.S. and Mexico as "very, very significant". It is possible that the two countries reached a basic agreement before Nielsen's departure, but the U.S. side wanted more troops deployed. They also made clear that Trump was dead set on the tariffs without dramatic action.
Those measures will include deploying Mexico's militarised National Guard security force to its southern border.
The Mexican Finance Ministry on the same day also said they blocked the bank accounts of 26 people for their alleged involvement in human trafficking.
But the threat appears to have worked both to bring Mexico to the negotiating table and to win concessions that the Mexican government had been reluctant to agree to, including cooperating with the U.S.to hold Central American asylum-seekers while they are awaiting their cases in the U.S.
Under the new deal, returned asylum seekers will spend long periods in Mexican cities such as Reynosa on the Texas border, where drug cartels frequently kidnap migrants.
In a shift from the past when most undocumented immigrants were men seeking work, a majority of recent arrivals are families or unaccompanied children fleeing violence.
Senator Joni Ernst, who represents the farming state of Iowa and had broken with Trump on the tariffs, said that her state was "breathing a sigh of relief" with the deal. "There isn't enough docks, warehouses, facilities for all the goods coming into the United States from Mexico right now".
"The US president is taking trade decisions that are in total violation of the WTO rules", Lamy said.
Chuck Schumer, the top Democrat in the Senate, mocked Trump's triumphant announcement of a deal to reduce illegal immigration. But the State Department's Undersecretary for Management Brian Bulatao has denied all their requests so far this year, saying they can display the flag in other places inside and outside the embassies instead, NBC News reports.
USMCA ratification is already uncertain in the U.S. Congress, and tariffs would make legislators even less likely to approve it. Richard Neal, the Democratic chair of the House of Representatives committee that oversees trade, has also said he would introduce legislation to stop the tariffs on Mexico.