Mexico's ruling party candidate Claudia Sheinbaum has won the presidential elections, according to exit polls released Monday.

The 61-year-old former Mexico City mayor won around 58% of votes, according to a representative statistical sample released by election officials on Monday.

The result puts her comfortably ahead of leading opposition rival Xochitl Galvez, who had 29%.

What did the Morena party say about the election victory?

"I won't fail you," Sheinbaum told supporters after preliminary results showed her achieving a landslide victory.

"I will become the first woman president of Mexico," she added.

Mexico's president-elect pledged to run a "fiscally responsible" administration that respects the Bank of Mexico's autonomy.

The leader of the ruling Morena party, outgoing President Andres Manuel Lopez Obrador, congratulated her on the win.

Morena national president Mario Delgado told the Milenio TV broadcaster that the party had won a simple majority in Congress, short of the two-thirds majority it would need to push constitutional reforms past the opposition and do away with oversight agencies it claims are wasteful.

Opposition candidates have said such changes would endanger Mexican democracy.

Currently, the Morena Party also holds 23 of Mexico's 32 governorships.

Election overshadowed by violence

The election was overshadowed after two people were killed in violence at polling centers on Sunday amid a campaign that has already seen 38 candidates murdered, including a local candidate who was fatally shot on Saturday night. The deadly incidents have raised concerns about the threat of warring drug cartels to democracy.

Voting was brought to a halt at one polling center after a person was killed in a shooting in Comeyoapan, a town in the state of Puebla, according to the state electoral authority.

Another death at a polling station in Tlanalapan, also in Puebla, was reported by the state attorney general.

Historic vote

Sunday's election saw the historic election of the country's first female president, with two women vying for the top job ahead of a man running a distant third.

When polls opened, Sheinbaum enjoyed a nearly 17-point advantage over opposition candidate Xochitl Galvez.

Sheinbaum has promised to continue the populist political program of popular outgoing President Andres Manuel Lopez Obrador, who is constitutionally barred from seeking another term in office.

Galvez, a former senator and tech entrepreneur, represents a coalition of opposition parties and has promised to change tack from Lopez Obrador's "hugs, not bullets" policy toward the country's ultra-violent drug cartels.

Cartel violence on voters' minds

Both the economy — which is struggling in the increasingly polarized country — and cartel violence are foremost on voters' minds according to opinion polls.

This would seem to come as no surprise in a campaign season marred by violence.

Dozens of candidates have been murdered since campaigning began for roughly 20,000 positions across the country — from the presidency and governorships, to both houses of Congress and various local posts.

In all, more than 450,000 people have been murdered since Mexico began fighting its war on drugs in 2006.

Thousands of soldiers have been deployed at polling stations around the country for Sunday's vote.

js, sdi/kb, sms (AFP, AP, Reuters, dpa)