Claudia Sheinbaum of Mexico's Morena ruling party made history on Sunday by being elected the country's first female president in a landslide victory, according to preliminary official results.

The 61-year-old former mayor of Mexico City, and a scientist by training, secured approximately 58-60% of the votes, as announced by the National Electoral Institute following a quick count.

Sheinbaum's lead was substantial, garnering over 30 percentage points more than her main opponent, Xochitl Galvez, and about 50 percentage points ahead of the only male candidate, centrist Jorge Alvarez Maynez.

Supporters gathered in Mexico City's main square, waving flags and celebrating Sheinbaum's victory with mariachi music. 

"I won't fail you," the president-elect said after preliminary official results emerged.

Despite occasional violence in regions terrorized by ultra-violent drug cartels, voters turned out in large numbers across the nation. Thousands of troops were deployed to ensure voter safety during a particularly violent electoral process that saw over two dozen aspiring politicians murdered.

Hours before the polls opened, authorities confirmed that a local candidate was murdered in a violent western state, adding to the at least 25 political hopefuls killed this election season.

In Puebla, a central Mexican state, two people were killed when unknown assailants attacked polling stations to steal papers, a local government security source told AFP. Voting was suspended in two municipalities in the southern state of Chiapas also due to violence.

Earlier in the day, Sheinbaum described the election as "historic". After casting her ballot, she revealed she voted for 93-year-old veteran leftist Ifigenia Martinez in recognition of her lifelong struggle.

"Long live democracy!" Sheinbaum declared.

After the polls closed, 61-year-old senator Galvez encouraged her supporters to vigilantly monitor the vote count, expressing concerns over competing against "authoritarianism and power."

Nearly 100 million people of Mexico's 129 million population were registered to vote.

Sheinbaum has pledged to continue outgoing President Andres Manuel Lopez Obrador's "hugs not bullets" strategy to address crime by tackling its roots. In contrast, Galvez had promised a tougher stance on cartel-related violence, stating that "hugs for criminals are over."

Since the Mexican government deployed the army to fight drug trafficking in 2006, over 450,000 people have been murdered and tens of thousands have gone missing.

Sheinbaum will also have to manage delicate relations with the neighboring United States, particularly concerning cross-border drug smuggling and migration.

In addition to electing a new president, Mexicans voted for members of Congress, several state governors, and numerous local officials, totaling more than 20,000 positions.