A projection based on votes counted at 7800 representative polling stations confirmed the victory of the 64-year-old in Sunday's elections, National Electoral Institute President Lorenzo Cordova said.

Lopez Obrador took between 53 and 53.8 per cent of the vote.

Conservative-centrist Ricardo Anaya received up to 22.8 per cent, while Jose Antonio Meade from outgoing President Enrique Pena Nieto's Institutional Revolutionary Party (PRI) had up to 16.3 per cent.

Meade and Anaya congratulated Lopez Obrador before the official results had been announced, wishing him "the greatest success."

The winner spoke of "a historic day."

"Peace and tranquility are the fruit of justice," Lopez Obrador said, pledging "a plan of reconciliation and peace for Mexico" and promising there would be "no dictatorship" under his government.

The electoral authority described the turnout as "massive" among the 89 million people eligible to vote.

Among the 3400 offices being contested were 500 seats in the Chamber of Deputies, 128 in the Senate, eight governorships and 1600 mayoralties.

Lopez Obrador's Morena party was expected to do well. Exit polls gave its candidate Claudia Sheinbaum as the new Mexico City mayor.

Voters were seen as having punished the PRI for a string of corruption scandals, sluggish economic growth of only about 2 per cent and the party's perceived inefficiency in combating the country's soaring crime rate.

Pena Nieto, whose approval ratings stood at only about 20 per cent, was limited by the constitution to a single term.

Former Mexico City mayor Lopez Obrador, who had already run for the presidency twice before, cast himself as an anti-establishment candidate prepared to crack down on corruption and to help the poor.

Despite lambasting the entrepreneurial elite as "a rapacious minority," he's excluded the possibility of expropriations and pledged guarantees to investors.

He's also pledged a less militarised, more social approach to fighting crime, including an amnesty to lower-level gang members.

Mexico recorded about 29,000 killings last year, the highest annual number since modern records started being kept two decades ago.

The electoral campaign was overshadowed by violence, with about 120 politicians assassinated over 10 months, according to risk consultant Etellekt.

Lopez Obrador's victory was expected by many to further worsen Mexico's already frosty relations with the US, whose president, Donald Trump, has slammed the country over illegal migration and pressured it to pay for a border wall.

The president-elect said he would seek "a relationship of friendship and cooperation" with Mexico's northern neighbour, but one based on "mutual respect."

Lopez Obrador was expected to be more assertive with Trump while seeking to reduce Mexico's dependency on US fuel and other trade.

Trump tweeted that he looked "very much forward to working with" Lopez Obrador. "There is much to be done that will benefit both the United States and Mexico!" the president added.

Australian Associated Press