Mexico City (AFP) - US President Donald Trump and Mexican president-elect Andres Manuel Lopez Obrador said Monday they had had a "great" first phone call, with the Latin American leftist offering to reduce US-bound migration.

Lopez Obrador, a fiery leftist who represents a clean break with Mexico's political establishment, won a sweeping election victory Sunday -- raising questions about the future of Mexico's crucial relationship with its giant northern neighbor.

The politician known as "AMLO" had vowed during the campaign to "put (Trump) in his place," at a time when the Republican president's anti-trade, anti-immigration policies have infuriated Mexico.

But the two men appear to have hit it off in their first phone call after Lopez Obrador's victory.

"I received a phone call from Donald Trump and we spoke for half an hour," Lopez Obrador wrote on Twitter, in one of his first messages as president-elect.

"I proposed exploring a universal deal (involving) development projects that would create jobs in Mexico and, by doing so, reduce migration and improve security," he added.

"The tone was respectful and our teams will be holding talks."

- 'Mexican Trump'? -

Trump also mentioned the phone call as he addressed reporters in the Oval Office.

"I think the relationship is going to be a very good one. We had a great talk," he said.

"I think he is going to try and help us with the border."

US-Mexican relations have been strained since Trump won election in 2016 after a campaign laced with anti-Mexican insults, attacks on the North American Free Trade Agreement (NAFTA), and promises to build a wall on the two countries' border and make Mexico pay for it.

That rhetoric fired up his supporters, but caused alarm in Mexico, which sends 80 percent of its exports to the United States and is deeply intertwined with its neighbor thanks to the 11.4 million Mexicans who live there.

US tariffs on Mexican steel and aluminum, Trump's "zero-tolerance" policy on undocumented immigrants, separation of migrant families and two abruptly canceled visits to Washington by current Mexican President Enrique Pena Nieto have only added to the tension.

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Some in Mexico fear Lopez Obrador's combative style will increase the strains. But others are holding out hope a change in leadership will help.

Commentators have drawn parallels between the two leaders: both are free-trade skeptics with populist tendencies who mobilized a disgruntled base with anti-establishment campaigns.

"AMLO is not going to pay for the wall, that's for sure," said Mark Weisbrot, co-director of the Center for Economic and Policy Research in Washington.

"But he has made it clear that he wants good relations with the US."

- Political shift -

Lopez Obrador, a sharp-tongued, silver-haired former Mexico City mayor who was making his third run for president, won with more than 53 percent of the vote, with nearly 64 percent of ballots counted, according to the latest official results.

It is the first time in Mexico's modern democracy that a candidate has won more than half the vote, and a resounding rejection of the two parties that have governed the country for nearly a century.

Lopez Obrador, 64, will be the country's first leftist president in recent history when he takes office on December 1.

His coalition -- led by the party he launched in 2014, Morena -- also won a majority in the lower house of Congress, and was within striking distance of doing the same in the Senate, according to exit polls.

And it was on track to win at least five of the nine governorships being decided.

Lopez Obrador successfully tapped voters' anger over a seemingly never-ending series of corruption scandals and violent crime that left a record 25,000 murders last year.

But he is a divisive figure in Mexico.

For his many critics, there was fear about what his promise of "deep change" will mean.

Some opponents have branded him a "tropical Messiah" who will install Venezuela-style policies that could wreck Latin America's second-largest economy.

There are lingering market jitters over a politician who clashed openly with the business sector during the campaign.

The Mexican stock market's key index lost 2.12 percent Monday, while the peso closed down 0.9 percent against the dollar.