RINCON DE CHAUTLA, MexicoRINCON DE CHAUTLA, Mexico (Reuters) - When the 56-year-old mother-in-law of David Sanchez Luna was tortured and killed after venturing out of her small Mexican community encircled by drug cartels, he let his seven- and ten-year-old daughters receive military-style weapons training.

Unable to send their children to school and too afraid to step out of their enclave of 16 mountain villages in the violence-plagued southwestern Guerrero state, residents say they have been left with little choice.

"They do this to prepare themselves to defend the family, their siblings and defend the village," said Sanchez Luna, a corn farmer in a rugged region which five years ago formed a self-defense "community police" militia to protect itself.

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The move by the villagers to offer arms training to school-age children shocked the nation and made global headlines last month after local media broadcast images of children as young as 6-years-old toting guns and showing off military maneuvers.

While elders in the mainly indigenous community near the city of Chilapa privately concede young kids would not be used to fight cartel gunmen, they say their gambit to get the help of far-away officials in Mexico City is borne of desperation.

Ten musicians from the area were ambushed and killed last month by suspected Los Ardillos cartel members after stepping out of the territory guarded by their self-defense militia, known as CRAC-PF. Their bodies were burnt, officials said.

The attack followed a spate of murders in recent year, including a beheading, that rattled the 6,500 residents whose lush land sits amid fertile poppy-growing farmland that feed Guerrero's heroin trade and supply routes to the United States.

The grisly murders and siege-like conditions facing residents go to the heart of cartel power and state failure in modern Mexico, where runaway violence tears at society's fabric.

"This is a public cry for help by a community that's been cornered," said Falko Ernst, an International Crisis Group (ICG) analyst. "They've been trying to get assistance by federal and state government, unsuccessfully, so they're trying to escalate the language to try to negotiate and get help."

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President Manuel Andres Lopez Obrador said those who arm children "should be ashamed of themselves" and denounced the use of children to grab attention.

Lopez Obrador's government has struggled to get a grip on gangs and violence, with a record 34,582 murders last year.

Residents remain deeply suspicious of regional authorities and the smattering of local policemen in their villages, who they accuse of being the eyes and ears of the Los Ardillos.

Parents say their children are forced to stop formal education once they reach about 12 years of age, as the middle schools are in territory controlled by the cartel.

Abuner Martinez, 16, stopped attending school a year ago after his father was kidnapped outside CRAC-PF territory, tortured, and then beheaded.

"I got scared at that moment. I didn't want to go to school," said Martinez, who now wields a shotgun as he guards a checkpoint.

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The Los Ardillos want to extort the farmers and force them to grow opium for the cartel, said Sanchez Luna's brother, Bernardino, who founded the CRAC-PF.

"We find ourselves under siege," he said.

CRAC-PF repelled a major attack by Los Ardillos in January 2019, but residents live in fear of the siren, a community alarm system, going off again.

Farmers tend their corn fields with shotguns slung on their backs, while armed CRAC-PF militiamen keep guard and patrol their territory round the clock. 

David Sanchez Luna's wife, Alberta, sobbed as she described receiving her mother's body riddled with torture marks.

"It's terrible what's happening to us," she said, wiping away tears.

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(Writing by Drazen Jorgic; Editing by Daniel Wallis)