Mexican opposition presidential candidate Xochitl Galvez, seen here displaying her ballot, later conceded defeat
Mexican opposition presidential candidate Xochitl Galvez, seen here displaying her ballot, later conceded defeat AFP

Congratulations poured in from around the world Monday after Claudia Sheinbaum was elected Mexico's first woman president, sparking hope for change in a country where gender-based violence has long been rife.

Flag-waving supporters sang and danced to mariachi music late into the night after the former Mexico City mayor won Sunday's election by a landslide.

Addressing cheering crowds, the 61-year-old thanked the "millions of Mexican women and men who decided to vote for us on this historic day."

Maria Fernanda Vela, 27, said it was "an inspiration that in such a male chauvinist country, a woman has taken the top job. It fills your heart with pride."

US President Joe Biden welcomed Sheinbaum's "historic election" and said he looked forward to working with her "in the spirit of partnership and friendship."

Canadian Prime Minister Justin Trudeau, another key North American ally, also offered congratulations and said he was ready to work closely with Sheinbaum to further strengthen relations.

Brazilian President Luiz Inacio Lula da Silva, a fellow leftist, hailed a "victory for democracy" and vowed to deepen economic ties between Latin America's two biggest economies.

Russian President Vladimir Putin and Ukraine's Volodymyr Zelensky were among other leaders offering congratulations.

Sheinbaum, a scientist by training, won around 58-60 percent of votes, according to preliminary official results from the National Electoral Institute, which estimated turnout at 60 percent.

That was more than 30 percentage points ahead of her main opposition rival Xochitl Galvez, and some 50 percentage points ahead of the only man running, centrist Jorge Alvarez Maynez.

Mexican women cheered the breaking of the highest political glass ceiling in a nation where around 10 women or girls are murdered every day.

"Our society is violent, sexist, misogynistic and Dr. Sheinbaum as president will really be able to help change not only the laws but society," said Lol-Kin Castaneda, 48, who waited late into the night to hear the winner speak.

"Mexico can't stand any more violence," she added.

Nearly 100 million people were registered to vote in the world's most populous Spanish-speaking country, home to 129 million people.

Sheinbaum owes much of her popularity to outgoing president Andres Manuel Lopez Obrador, a fellow leftist and mentor who has an approval rating of more than 60 percent but is only allowed to serve one term.

Lopez Obrador, who will hand over the presidency in October, hailed his handpicked successor's victory as a "historic event."

In another win for the ruling party, its candidate Clara Brugada was elected mayor of Mexico City, one of the country's most important political jobs, preliminary results showed.

In a nation where politics, crime and corruption are closely entangled, drug cartels went to extreme lengths to ensure that their preferred candidates win.

Thousands of troops were deployed to protect voters on election day, following a bloody electoral season that saw more than two dozen aspiring local politicians murdered.

The violence continued after polls closed, with a local mayoral candidate killed in the country's south late Sunday, authorities said.

In the central Mexican state of Puebla, two people died after unknown persons attacked polling stations Sunday to steal papers, a local government security source told AFP.

Voting was suspended in two municipalities in the southern state of Chiapas because of violence.

"Despite a mostly free and peaceful voting day, organized crime and socio-political conflicts tainted the electoral process," said Arantza Alonso, an analyst at risk intelligence company Verisk Maplecroft.

"Organized crime's ongoing influence on Mexican elections and governance structures will continue to undermine public security and democratic governance," she said.

Sheinbaum has pledged to continue the outgoing president's "hugs not bullets" strategy of tackling crime at its roots.

Galvez had vowed a tougher approach to cartel-related violence, declaring "hugs for criminals are over."

Sheinbaum will also have to manage delicate relations with the neighboring United States, in particular the vexed issues of cross-border drug smuggling and migration.

Ties could become even more challenging if Donald Trump returns to the White House.

If the Republican wins the US election in November, he is "expected to double down on his hardline stance on immigration, trade, and drugs," said Michael Shifter, an expert at the Inter-American Dialogue think tank in Washington.

Mariachis play as supporters of presidential candidate Claudia Sheinbaum celebrate in Mexico City
Mariachis play as supporters of presidential candidate Claudia Sheinbaum celebrate in Mexico City AFP
Members of Mexico's National Guard patrol in the violence-hit southern state of Guerrero on election day
Members of Mexico's National Guard patrol in the violence-hit southern state of Guerrero on election day AFP