Gisela Gaytán had just arrived at an event on the first day of her mayoral campaign in central Mexico’s industrial heartland when the gunfire broke out.

Moments later, her lifeless body laid crumpled in a pool of blood.

The assassination in broad daylight of Ms. Gaytán, a 37-year-old lawyer, reflects a gruesome trend in this year’s general election in Mexico. She figures among the 36 people killed since last summer while seeking public office, according to a New York Times analysis, making this one of the most blood-soaked election cycles in recent memory.

The candidate killings point to a threat at the core of Mexico’s democracy. Voters are preparing to cast ballots next month in a spirited election that could produce the country’s first female president, a milestone in the world’s largest Spanish-speaking country.

But analysts and law enforcement officials say that emboldened cartels are spreading fear in races at the local level as they expand their reach into extortion rackets, migrant trafficking and food production.

Heightening the sense of terror, not only candidates but their family members are being increasingly targeted, with at least 14 such relatives killed in recent months. Some cases have been especially gruesome; in Guerrero state, the dismembered bodies of a candidate for city council and his wife were found this month.