Claudia Sheinbaum has declared that she will become Mexico's first female president, in her victory speech after Sunday's election.

The former Mexico City mayor, from the ruling leftist party Morena, delivered the speech after election authorities announced that preliminary results showed she received between 58 to 60 percent of the vote.

Sheinbaum won by a wide margin over her nearest rival, Xochitl Galvez, a former senator and candidate for the opposition coalition.

The election was effectively a contest between the two candidates.

Sheinbaum said that for the first time in the republic's 200-year history, she will become Mexico's first female president. She added that it is a victory not just for her but for all women.

Sheinbaum had the support of incumbent President Lopez Obrador, who has maintained high approval ratings. During the election campaign, she called for continuing Obrador's social welfare and security policies.

She will take office amid a wave of violent incidents, such as murders and kidnappings by drug cartels and others.