President Donald Trump talks with reporters before departing on Marine One for the Air Force Academy graduation ceremony. Picture: Evan Vucci/AP

Sterling, Virginia - With his threatened Mexican tariffs now on the backburner, President Donald Trump was looking to claim victory even as some of his Democratic challengers for the White House criticized him for overselling.

"There is now going to be great cooperation between Mexico & the USA, something that didn't exist for decades," Trump tweeted before spending a second day at his Virginia golf course.

"However," he added, "if for some unknown reason" that doesn't happen, "we can always go back to our previous, very profitable, position of Tariffs." Business leaders and many Republicans had urged Trump against the tariffs, warning they would drive up consumer prices, hinder the economy and compromise the ratification of an updated North American trade deal.

The tweets came amid questions about just how much of the deal - announced with great fanfare Friday - was really new. It included a commitment from Mexico, for instance, to deploy its new National Guard to the country's southern border with Guatemala. Mexico, however, had already intended to do that before Trump's latest threat and had made that clear to US officials. Mexican officials have described their commitment as an accelerated deployment.

The US also hailed Mexico's agreement to embrace the expansion of a program implemented earlier this year under which some asylum-seekers are returned to Mexico as they wait out their cases. But US officials had already been working to expand the program, which has already led to the return of about 10 000 to Mexico, without Mexico's public embrace.

"The president has completely overblown what he reports to have achieved. These are agreements that Mexico had already made, in some cases months ago," said Democratic presidential candidate Beto O'Rourke, speaking on ABC's "This Week." ''They might have accelerated the time table, but by and large the president achieved nothing except to jeopardize the most important trading relationship that the United States of America has."

Another 2020 candidate, Sen. Bernie Sanders of Vermont, chastised Trump for using tariffs as a threat and operating a "trade policy based on tweets."

"I think what the world is tired of and what I am tired of is a president who consistently goes to war, verbal war with our allies, whether it is Mexico, whether it is Canada," he said.

But acting Homeland Security Secretary Kevin McAleenan, speaking on "Fox News Sunday" insisted "all of it is new," including the agreement to dispatch around 6,000 National Guard troops — a move Mexico has described as an "acceleration."

A Mexican Army soldier walks on the highway, near an immigration checkpoint in Tapachula, Chiapas state. Picture: Marco Ugarte/AP

"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," he said, adding that "people can disagree with the tactics" but that "Mexico came to the table with real proposals" that will be effective, if implemented.

Trump echoed the same in his tweets, insisting the deal was being misrepresented and demanding more credit from the press.

"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," he wrote, claiming that if former President Barack Obama had made the deals he has, "the Corrupt Media would be hailing them as Incredible, & a National Holiday would be immediately declared."

Migrants travel from Guatemala to Mexico on a raft, pushed with a pole by its operator who charges his passengers, across the Suchiate River near Ciudad Hidalgo, Mexico. Picture: Marco Ugarte/AP

He also teased the idea that more was agreed to than was announced Friday, saying that "some things" and "one in particular" that had been left out of the release but would be "announced at the appropriate time."

He could have been referring to discussion about Mexico becoming a "safe third country," which would make it harder for asylum-seekers who pass through the country to claim refuge in the US The idea, which Mexico has long opposed, was discussed during negotiations. But Mexican Foreign Minister Marcelo Ebrard has said Mexico did not agree to it.

Mexico's ambassador in Washington nonetheless said her country is committed to working with the US and that discussions will continue.

A migrant swims from Guatemala to Mexico across the Suchiate River near Ciudad Hidalgo, Mexico. Picture: Marco Ugarte/AP

"We want to continue to work with the U.S. very closely on the different challenges that we have together. And one urgent one at this moment is immigration," said Martha Barcena. 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 soldier briefly questions a Honduran migrant who just crossed the Suchiate River, Mexico's natural border with Guatemala, before allowing him to go. Picture: Marco Ugarte/AP

The US, she said, wants to see the number of migrants crossing the border return to levels seen in 2018. US Border Patrol last week announced it had apprehended more than 132 000 people at the border in May, including a record 84,542 adults and children traveling together, straining federal resources and leaving officials struggling to provide basic housing and health care.

AP