Claudia Sheinbaum makes history as Mexico's first female president

Sheinbaum earned between 58 60 per cent of the vote, preliminary results show

Claudia Sheinbaum celebrates her election win with supporters in Mexico City. Polls show she was more than 30 percentage points of her nearest rival. AFP

Claudia Sheinbaum has secured a landslide election win to become Mexico's first female president, making history in a country plagued by rampant criminal and gender-based violence.

Supporters sang and danced to mariachi music in the main square of Mexico City to celebrate the victory of Ms Sheinbaum, a member of the ruling Morena party. She was previously mayor of Mexico City.

"I want to thank the millions of Mexican women and men who decided to vote for us on this historic day," Ms Sheinbaum, 61, told the crowd. "I won't fail you."

She also thanked election rival Xochitl Galvez, who conceded defeat on Monday.

Ms Sheinbaum, a scientist by training, won between 58 and 60 per cent of votes, preliminary results from the National Electoral Institute showed. It estimated turnout to be 60 per cent.

The preliminary results showed Ms Sheinbaum was more than 30 percentage points ahead of Ms Galvez, and about 50 percentage points ahead of the only male candidate running in the election, centrist Jorge Alvarez Maynez.

Supporters of new Mexico President Claudia Sheinbaum await her arrival at the main square in Mexico City. AP

Voters flocked to polling stations across the country, despite sporadic violence in areas terrorised by violent drug cartels. Thousands of troops were sent to protect voters amid a particularly bloody electoral process in which more than two dozen aspiring local politicians were killed.

"Our society is violent, sexist, misogynistic. Dr Sheinbaum as President will really be able to help change not only the laws but society," said Lol-Kin Castaneda, 48. "Mexico can't stand any more violence."

The election of a female president is a remarkable leap forward for a country where about 10 women or girls are killed every day. "A female president will be a transformation for this country, and we hope that she does more for women," said Clemencia Hernandez, 55, who works as a cleaner in Mexico City.

A woman casts her ballot in Mandinga, Mexico. Election authorities estimate turnout to be 60 per cent. Reuters

"Many women are subjugated by their partners. They're not allowed to leave home to work," she added.

Daniela Perez, 30, said that having a woman in charge of Mexico was "something historic", even though Ms Sheinbaum and Ms Galvez are not "totally feminist".

"We'll have to see their positions on improving women's rights, resolving the issue of femicides," said Ms Perez, a logistics company manager.

Nearly 100 million people were registered to vote in Mexico, which has a population of about 129 million.

Ms Sheinbaum owes much of her popularity to outgoing president Andres Manuel Lopez Obrador, a fellow leftist and her mentor. He had an approval rating of more than 60 per cent but was only allowed to serve one term.

Mr Lopez Obrador congratulated Ms Sheinbaum with "all my affection and respect". As well as being the first woman to lead Mexico, "she is also the president with possibly the most votes obtained in the history of our country", he said.

Ms Sheinbaum said she voted for 93-year-old veteran leftist, Ifigenia Martinez, in recognition of her struggle.

In a nation where politics, crime and corruption are closely entangled, drug cartels went to extreme lengths to ensure their preferred candidates won. Hours before polls opened, a candidate in a local election was killed in the western Michoacan state, authorities said.

At least 25 political hopefuls were killed during election season, official figures show.

In the central Mexican state of Puebla, two people died in an attack on polling stations, a government security source told AFP. Voting was suspended in two municipalities in the southern state of Chiapas due to violence.

Ms Sheinbaum has pledged to continue Mr Lopez Obrador's controversial "hugs not bullets" strategy of tackling crime.