Claudia Sheinbaum was elected Mexico's first woman president by a landslide Sunday, preliminary official results showed, making history in a country plagued by rampant criminal and gender-based violence.

Crowds of flag-waving supporters sang and danced to mariachi music in Mexico City's main square celebrating the ruling party candidate's victory.

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, long-shot centrist Jorge Alvarez Maynez.

Voters had flocked to polling stations across the Latin American nation, despite sporadic violence in areas terrorized by ultra-violent drug cartels.

Thousands of troops were deployed to protect voters, following a particularly bloody electoral process that has seen more than two dozen aspiring local politicians murdered.

Earlier, Sheinbaum hailed what she called a "historic" election day.

After casting her ballot, she revealed she had not voted for herself but for a 93-year-old veteran leftist, Ifigenia Martinez, in recognition of her struggle.

"Long live democracy!" Sheinbaum declared.

After the polls closed, Galvez urged her followers to closely monitor the count.

"We are competing against authoritarianism and power and they are capable of anything," said the 61-year-old senator and businesswoman with Indigenous roots.

Bd pratidin English/Lutful Hoque