Results on Monday showed Claudia Sheinbaum was elected Mexico's first woman president by a landslide.

The National Electoral Institute announced after a quick count that Sheinbaum won around 58 to 60 percent of the vote, more than 30 percentage points ahead of her main opposition rival Xochitl Galvez, also a woman.

Sheinbaum later announced that her opponents had conceded the race to her.

Victory for Sheinbaum was a major step for Mexico, a country known for its macho culture and home to the world's second biggest Roman Catholic population, which for years pushed more traditional values and roles for women.

Sheinbaum was also the first woman to win a general election in the United States, Mexico or Canada.

The election was also the biggest in the country’s history. More than 20,000 congressional and local positions were up for grabs, according to the National Electoral Institute.

Sheinbaum has a complicated path ahead. She must balance promises to increase popular welfare policies while inheriting a hefty budget deficit and low economic growth.

She has vowed to improve security but has given few details while the election was the most violent in Mexico's modern history with 38 candidates murdered.

Many analysts say organised crime groups expanded and deepened their influence during outgoing President Lopez Obrador's term.

More people have been killed - over 185,000 - during the mandate of Lopez Obrador than during any other administration in Mexico's modern history, although the homicide rate has been inching down. (Agencies)