On Saturday, a New York Times report, citing officials from both countries familiar with the negotiations, said most of Friday's deal had already been sketched out in March, when Mexico agreed to deploy its National Guard throughout the country, with priority given to the southern border.
The governments of Brazil, Panama and Guatemala did not immediately reply to requests for comment.
Another part of the deal was Mexico's agreement to deploy 6,000 National Guard servicemen to Mexico's southern border and across the country in order to curb the influx of immigrants crossing into the USA illegally. The administration has yet to reveal the details of any such provision, and Mexican officials say no agreement on farm goods was reached as part of the talks.
Officials in the Mexican border states of Sonora, south of the USA states of Arizona and New Mexico, and Tamaulipas, south of Texas, said they were unaware of plans to expand the number of border crossings where the asylum seekers must be returned to Mexican territory to await processing.
The president spent the weekend and Monday morning defending the U.S. -Mexico agreement on Twitter against criticisms the deal does not include anything new.
Trump said that if his predecessor, Barack Obama, made the deal he made with Mexico, the media would declare a "National Holiday" in his honor. USA officials had been working to expand the program, which has led to the return of about 11,000 to Mexico without Mexico's public embrace.
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The president went on to argue that Mexico had not historically been cooperative, but he believed a turning point had been reached.
"Those crossing the US southern border to seek asylum will be rapidly returned to Mexico where they will await their adjudication of their asylum claims", he said.
Trump echoed the same in his tweets, insisting the deal was being misrepresented and demanding more credit from the press.
He has also dangled the prospect of renewing his tariff threat if the US ally doesn't cooperate to his liking. There is now going to be great cooperation between Mexico & the U.S., something that didn't exist for decades.
Mexico's ambassador in Washington, meanwhile, said her country was committed to cooperating with the USA and that discussions would continue over the coming 90 days. But the president is not backing down from his initial threat, warning that should the deal not receive support in a vote from Mexican leadership, he'll go right back to tariffs.
"Now that that problem is solved, I'm sure we won't be hearing any more about it in the future", Schumer added.
"The scale, the effort, the commitment here is very different from what we were able to achieve back in December", he responded to a journalist's question about what was actually new in the agreement. "It is an immigration agreement, not a commercial one". She told CBS' "Face the Nation" that the countries' "joint declaration of principles ... gives us the base for the road map that we have to follow in the incoming months on immigration and cooperation on asylum issues and development in Central America". A law enforcement group of police officers, Marines, Military Police and immigration officials arrived at the area to intercept a caravan of migrants that had earlier crossed the Mexico - Guatemala border.
On Saturday, Mexico's foreign minister, Marcelo Ebrard, tweeted that the deal should boost economic growth and therefore demand for US agricultural products, but he also stopped short of saying that the deal contained a commitment on Mexico's part to purchase more goods from the United States.