"We have been trying to get some of these Border Actions for a long time, as have other administrations, but were not able to get them, or get them in full, until our signed agreement with Mexico", Trumptweeted.
USA border officers apprehended more than 132,000 people crossing from Mexico in May, the highest monthly level since 2006.
As the USA prepares for the immediate expansion of the Migrant Protection Protocols (MPP) program - dubbed "Remain in Mexico" - Pompeo said us authorities have increased their capacity of returning non-Mexican migrants who claim asylum at ports of entry along the southern border to Mexico.
Mr Ebrard said the U.S. side also wanted to designate Mexico as a "safe third country", which would have required Mexico to take in asylum seekers heading for the USA and process their claims on its own soil. "We do not anticipate a problem with the vote but, if for any reason the approval is not forthcoming, Tariffs will be reinstated", he wrote.
"Importantly, some things not mentioned in yesterday's press release, one in particular, were agreed upon".
Under the deal, the United States will expand the "Remain in Mexico" policy, officially known as the Migrant Protection Protocol, under which asylum seekers are required to stay in Mexico while USA immigration authorities review their applications.
On Friday, the tariffs were called off, after the United States and Mexico announced an agreement on immigration.
"They might have accelerated the timetable but by and large the president achieved nothing except to jeopardize the most important trading relationship that the United States of America has".
But as of Sunday night, US -bound asylum seekers were not yet being sent back to additional Mexican border towns, three Mexican officials said.
The deal will also see Mexico deploy the National Guard police force to its southern border, where many Central American migrants enter Mexico.
"This is likely to have only a small impact on solving the root causes of Central American migration because numerous components are things Mexico had already said they would do", Schumer said on Twitter.
In February, Mr Trump declared an emergency on the US-Mexico border, saying it was necessary in order to tackle what he described as a crisis.
The New York Timesreported over the weekend that officials from the us and Mexico said several terms in the new pact were actually agreed to last December, not in last week's negotiations between the two countries, a report Trump dismissed.
Marta Barcena Coqui, the Mexican ambassador to the United States, said in an interview with CBS' "Face the Nation" on Sunday that Mexican officials had agreed to take steps to reduce illegal immigration "to previous levels that we had maybe past year or in 2018".
Mexican officials have not confirmed any new agreement on agricultural products.
In total, there are 39 new cars and trucks built by US companies in Mexico and imported to the States.
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