Climate scientist and former Mexico City Mayor Claudia Sheinbaum held an irreversible lead Sunday in the race that would make her Mexico's first female president, according to an official quick count.

The National Electoral Institute's president said Sheinbaum had between 58.3% and 60.7% of the vote, according to a statistical sample. Opposition candidate Xóchitl Gálvez had between 26.6% and 28.6% of the vote and Jorge Álvarez Máynez had between 9.9% and 10.8% of the vote.

The governing party candidate campaigned on continuing the political course set over the last six years by her political mentor, President Andrés Manuel López Obrador.

His anointed successor, the 61-year-old Sheinbaum led the campaign wire-to-wire despite a spirited challenge from Gálvez.

This was the first time in Mexico that the two main opponents were women.

This, as heat, violence and polarization continued right through election day.

People turned out to vote in the township of Cuitzeo, in the western state of Michoacán, despite the fact that a town council candidate was shot to death by two hitmen aboard a motorcycle just hours before the election.

Residents voted under a heavy police guard — but later passed by the home of murdered candidate Israel Delgado to light a candle for the well-known local politician at an improvised altar on his doorstep.

Nationwide, voting was largely peaceful, but it appeared that even if Sheinbaum indeed wins, she is unlikely to enjoy the kind of unquestioning devotion that outgoing López Obrador has enjoyed. Both belong to the governing Morena party.

In Mexico City's main colonial-era main plaza, the Zocalo, Sheinbaum's lead didn't initially draw the kind of cheering, jubilant crowds that greeted López Obrador's victory in 2018.

Fernando Fernández, a chef, 28, joined the relatively small crowd, hoping for a Sheinbaum victory, but even he acknowledged there were problems.

"You vote for Claudia out of conviction, for AMLO," Fernández said, referring to López Obrador by his initials, as most Mexicans do. But his highest hope is that Sheinbaum can "improve what AMLO couldn't do, the price of gasoline, crime and drug trafficking, which he didn't combat even though he had the power."

Also in the crowd, Itxel Robledo, 28, a business administrator, expressed hope that Sheinbaum would do what López Obrador didn't. "What Claudia has to do is put professionals in every area."

Elsewhere in the city, Yoselin Ramírez, 29, said she voted for Sheinbaum, but split her vote for other posts because she didn't want anyone holding a strong majority.

"I don't want everything to be occupied by the same party, so there can be a little more equality," she said without elaborating.

The main opposition candidate, Gálvez, a tech entrepreneur and former senator, tried to seize on Mexicans' concerns about security and promised to take a more aggressive approach toward organized crime.

Nearly 100 million people were registered to vote, but turnout appeared to be slightly lower than in past elections. Voters were also electing governors in nine of the country's 32 states, and choosing candidates for both houses of Congress, thousands of mayorships and other local posts, in the biggest elections the nation has seen and ones that have been marked by violence.

The elections were widely seen as a referendum on López Obrador, a populist who has expanded social programs but largely failed to reduce cartel violence in Mexico. His Morena party currently holds 23 of the 32 governorships and a simple majority of seats in both houses of Congress. Mexico's constitution prohibits the president's reelection.

Both major presidential candidates were women, and either would be Mexico's first female president. A third candidate from a smaller party, Jorge Álvarez Máynez, trailed far behind in opinion polls.

Sheinbaum promised to continue all of López Obrador's policies, including a universal pension for the elderly and a program that pays youths to apprentice.

Gálvez, whose father was Indigenous Otomi, rose from selling snacks on the street in her poor hometown to start her own tech firms. A candidate running with a coalition of major opposition parties, she left the Senate last year to focus her ire on López Obrador's decision to avoid confronting the drug cartels through his "hugs not bullets" policy. She pledged to more aggressively go after criminals.

The persistent cartel violence and Mexico's middling economic performance were the main issues on voters' minds.

Julio García, a Mexico City office worker, said he was voting for the opposition in Mexico City's central San Rafael neighborhood. "They've robbed me twice at gunpoint. You have to change direction, change leadership," the 34-year-old said. "Continuing the same way, we're going to become Venezuela."

On the fringes of Mexico City in the neighborhood of San Andres Totoltepec, electoral officials filed past 34-year-old homemaker Stephania Navarrete, who watched dozens of cameramen and electoral officials gathering where frontrunner Claudia Sheinbaum was set to vote.

Navarrete said she planned to vote for Sheinbaum despite her own doubts about López Obrador and his party.

"Having a woman president, for me as a Mexican woman, it's going to be like before when for the simple fact that you say you are a woman you're limited to certain professions. Not anymore."

She said the social programs of Sheinbaum's mentor were crucial, but added that deterioration of cartel violence in the past few years was her primary concern in this election.

"That is something that they have to focus more on," she said. "For me security is the major challenge. They said they were going to lower the levels of crime, but no, it was the opposite, they shot up. Obviously, I don't completely blame the president, but it is in a certain way his responsibility."

In Iztapalapa, Mexico City's largest borough, Angelina Jiménez, a 76-year-old homemaker, said she came to vote "to end this inept government that says we're doing well and (still) there are so many dead."

She said the violence plaguing Mexico really worried her so she planned to vote for Gálvez and her promise to take on the cartels. López Obrador "says we're better and it's not true. We're worse."

López Obrador claims to have reduced historically high homicide levels by 20% since he took office in December 2018. But that's largely a claim based on a questionable reading of statistics. The real homicide rate appears to have declined by only about 4% in six years.

Just as the upcoming November rematch between President Biden and former President Donald Trump has underscored deep divisions in the U.S., Sunday's election revealed how severely polarized public opinion is in Mexico over the direction of the country, including its security strategy and how to grow the economy.

Beyond the fight for control of Congress, the race for Mexico City mayor - a post now considered equivalent to a governorship - is also important. Sheinbaum is just the latest of many Mexico City mayors, including López Obrador, who went on to run for president. Governorships in large, populous states such as Veracruz and Jalisco are also drawing interest.

Polls closed at 6 p.m. in most of Mexico.

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