Presidents Donald Trump and Andres Manuel Lopez Obrador each declared the deal averting US tariffs on Mexico a win on Saturday, as markets breathed a sigh of relief - though rights groups condemned what they called a draconian crackdown on migration.

Lopez Obrador said the bottom line on the last-minute deal reached Friday night was simple. "There will not be an economic or financial crisis in Mexico on Monday," he said.

Economists had warned the pain of Trump's threatened tariffs - set to start at 5 percent on Monday and rise incrementally to 25 percent by October - and Mexico's likely retaliatory measures would have been acute for both countries, with potentially global spillover.

Instead, the countries hammered out a deal in which Mexico agreed to bolster security on its southern border and expand its policy of taking back migrants, most of them from violence-riven Guatemala, Honduras and El Salvador, as the US processes their asylum claims.

Trump hailed it as a victory, after a week of terrifying his southern neighbor, whose economy depends heavily on exports to the US. "Mexico will try very hard, and if they do that, this will be a very successful agreement for both the United States and Mexico!" he tweeted early Saturday.

The relief was palpable in the Mexican border city of ­Tijuana, where Lopez Obrador led a rally attended by several thousand people to celebrate the deal and "the friendship of the people of Mexico and the United States."

However, the leftist leader - who said he had just spoken to Trump on the phone - also warned his American counterpart that it was not enough for Mexico to tighten its borders, saying Washington also needed to invest in economic development in Central America to stem the exodus from the region.

"The solution cannot be found in just closing borders or coercive measures. The only solution is to fight the lack of opportunity and poverty so that migration is optional," he said, speaking on a stage set up, with seeming symbolism, next to a McDonald's five blocks from the border.

The New York Times ­reported Saturday that most of the measures that Mexico signed onto in Friday's deal had already been agreed upon in prior negotiations.

Some advocacy groups in Mexico criticized the deal, saying the plan to deploy the newly created National Guard to the southern border would militarize a humanitarian problem and result in mass detentions of innocent women and children.

The deal criminalizes migration, said activist Luis Rey Villagran of the Center for Human Dignity.

"In this agreement, the migrants are currency," he said. "The National Guard should be combatting drug traffickers, not focusing on stopping children and women who are trying to fulfill their dreams."

Some opponents accused Lopez Obrador of playing into Trump's hands. "It will make Donald Trump so happy to say he didn't have to build his border wall because Mexico is now the wall," tweeted Mexican writer Esteban Illades.