Xochitl Galvez and Claudia Sheinbaum Pardo AFP

Attack violent crime at its roots or go to war with powerful drug cartels? Mexican presidential candidates are offering contrasting strategies to deal with rampant insecurity.

Stopping the spiral of bloodshed that has seen around 450,000 people murdered across the Latin American country since 2006 is a priority for voters ahead of the June 2 election, surveys show.

Ruling-party candidate Claudia Sheinbaum wants to continue outgoing President Andres Manuel Lopez Obrador's strategy of addressing the causes of crime.

This controversial approach, which the left-wing populist calls "hugs not bullets," aims to reduce insecurity by combating poverty and inequality.

"Instead of declaring war (on drug cartels), we build peace. That's the big difference between the opposition and us," Sheinbaum, who enjoys a significant lead in opinion polls, said recently.

Her main rival Xochitl Galvez has put insecurity at the heart of her campaign, which she launched in March in Fresnillo, the city considered by its residents to be the most dangerous in Mexico.

"Hugs for criminals are over," said the outspoken entrepreneur and senator, who is competing with Sheinbaum to become the country's first woman president.

"To have a Mexico without fear, we're going to restrain the most violent and aggressive criminal organizations in our country," she added.

Gangs such as notorious drug lord Joaquin "El Chapo" Guzman's Sinaloa Cartel and its arch-rival, the Jalisco New Generation Cartel, control swathes of Mexico.

They are involved not just in drug trafficking but myriad criminal activities including people smuggling, extortion and fuel theft.

More than 100,000 people are missing across the country, where murders and kidnappings are daily occurrences.

Mexico's homicide rate has remained above 23 per 100,000 inhabitants since 2016, higher than the Latin American average, according to the InSight Crime think-tank.

Galvez has pledged to capture most-wanted criminals, recruit more police and ensure that they receive an adequate salary, in a country where corruption is considered rife among poorly paid security personnel.

She has vowed to double the size of the National Guard, withdraw soldiers from civilian projects to focus on fighting criminal groups, and to build a new maximum security prison.

Sheinbaum has also pledged to strengthen the National Guard as well as Mexico's intelligence agencies, and to improve coordination with police and prosecutors.

"The difference between both of them is that Xochitl thinks that she needs to go after the bad guys more than Sheinbaum," Carlos Ramirez, a political risk expert at consultancy firm Integralia Consultores, said at a roundtable hosted by the Wilson Center.

Experts say that whoever wins the election faces a difficult balancing act to meet voters' expectations for less crime while respecting for rights.

People want a tough approach to crime but not "abuse," said Raul Benitez, an expert in security and organized crime at the Casede think tank.

"You don't fight crime by attacking poverty. You do it by attacking criminals with the right strategy," he added.

That requires coordination with judges, police, prosecutors and intelligence agencies, said Benitez, who noted Sheinbaum's success doing so as mayor of Mexico City from 2018-2023.

Some 41 percent of Mexicans see insecurity as the "most urgent" challenge for the next government, according to a survey by the newspaper El Financiero.

In Tijuana, a crime-plagued city on the border with the United States, 47-year-old teacher Cristian Castro believes that locking up criminals "doesn't attack the causes."

Enedina Galvez, a 34-year-old Mexican-American, wants candidates to consider decriminalizing drugs -- an idea absent from the campaign.

While Galvez has raised the issue of insecurity more than Sheinbaum, she is lagging well behind Sheinbaum in opinion surveys.

According to an average of polls compiled by the firm Oraculus, Sheinbaum has 59 percent of voter support, while Galvez is in second place with 35 percent.