Mexico's ruling party declared Claudia Sheinbaum the winner of the presidential election by a "large margin" after polls closed on Sunday, putting her on course to be the country's first woman president.

Pollster Parametria forecast Sheinbaum winning a landslide 56 percent of the vote, according to their exit polls, with opposition candidate Xochitl Galvez at 30 percent.

Four other exit polls also said Sheinbaum was set to win.

Provisional results will trickle in over coming hours. Galvez has not conceded and told her supporters to be patient for the official results.

A victory for Sheinbaum would represent a major step for Mexico, a country known for its macho culture. The winner is set to begin a six-year term on Oct. 1.

"I never imagined that one day I would vote for a woman," 87-year-old Edelmira Montiel, a Sheinbaum supporter in Mexico's smallest state Tlaxcala, said earlier on Sunday.

"Before we couldn't even vote, and when you could, it was to vote for the person your husband told you to vote for. Thank God that has changed and I get to live it," Montiel added.

Sheinbaum's ruling MORENA party has also declared its candidate the winner of the Mexico City mayorship race, one of the country's most important races, though the opposition has disputed that and claims its own nominee won the contest.

Sunday's vote was marred by the killing of two people at polling stations in Puebla state, adding to multiple attacks that have made Mexico's largest-ever elections also the most violent in its modern history. Some 38 candidates were killed, with the violence stoking concerns about the threat of warring drug cartels to democracy.

Security fears dominated the concerns of many voters at the polls and Sheinbaum will be tasked with confronting organized crime. More people have been killed during the mandate of outgoing President Andres Manuel Lopez Obrador than during any other administration in Mexico’s modern history, although the homicide rate has come down over his term.

Pre-election polls indicated that MORENA and its allies will likely fall short of securing a two-thirds majority in Congress. That would make it more difficult for Sheinbaum to push constitutional reforms past opposition parties.

Among the new president's challenges will be tense negotiations with the United States over the huge flows of U.S.-bound migrants crossing Mexico and security cooperation over drug trafficking at a time when the U.S. fentanyl epidemic rages.

Mexican officials expect these negotiations to be more difficult if the U.S. presidency is won by Donald Trump in November. Trump has vowed to impose 100 percent tariffs on Chinese cars made in Mexico and said he would mobilize special forces to fight the cartels.

At home, the next president will be tasked with addressing electricity and water shortages and luring manufacturers to relocate as part of the nearshoring trend, in which companies move supply chains closer to their main markets.

The election winner also will have to wrestle with what to do with Pemex, the state oil giant that has seen production decline for two decades and is drowning in debt.

Sheinbaum has promised to expand welfare programs, though Mexico has a large deficit this year and sluggish GDP growth of just 1.5 percent expected by the central bank next year.

Lopez Obrador has loomed over the campaign, seeking to turn the vote into a referendum on his political agenda. Sheinbaum has rejected opposition claims that she would be a "puppet" of Lopez Obrador, though she has pledged to continue many of his policies including those that have helped Mexico's poorest.

Political analyst Viri Rios said she thought it was pure sexism for people to believe Sheinbaum was going to be a puppet.

"It's unbelievable that people cannot believe she's going to be making her own decisions, and I think that's got a lot to do with the fact that she's female," she said.

(Reuters)

Claudia Sheinbaum, Mexico City, June 2, 2024. (Reuters)

Mexico's Sheinbaum seen winning landslide, set to be first female president