The women and children were attacked as they moved in a small convoy of three SUVs between the states of Sonora and Chihuahua.
The LeBaron's Mormon community is only seventy miles south of Douglas, Arizona.
The victims are reportedly all dual US-Mexican citizens who live in a community which broke away from the mainstream Church of Jesus Christ of Latter-day Saints decades ago.
President Donald Trump has extended an offer to helpMexico wage a "war" to eliminate drug cartels, after at least nine Americans were killed during a cartel shooting in the Mexican border state of Sonora.
Mexican President Andres Manuel Lopez Obrador is blamed for the growing power and impunity of the drug cartels, to which he has taken a non-confrontational approach.
"We declared war, and it didn't work", he said, referring to the policies of previous administrations. "That is not an option".
In explaining his decision to for a halt for to nicknames for the faith, church president Russell M. Nelson said the Lord impressed upon him the importance of the full name and that leaving it out was "a major victory for Satan".
"This is the time for Mexico, with the help of the United States, to wage WAR on the drug cartels and wipe them off the face of the earth", Trump tweeted.
The US ambassador to Mexico, Christopher Landau, travelled to Sonora earlier on Monday, he said on Twitter.
A family member, Kendra Lee Miller, tells NBC News that 8-month old twins were killed in the attack.
Family members of the victims say they are in complete shock.
"It was a massacre", Julian LeBaron, an activist who has denounced criminal groups in the area, told Mexican radio network Formula.
"We just can't believe that this has actually happened to our family, this seems like a bad dream".
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"We still suffer from insecurity and violence", he said.
Eight children survived, five with bullet wounds.
One woman was killed after she apparently jumped out of her vehicle and waved her hands to show she wasn't a threat, according to family members and prosecutors.
"This is for the record", says a male voice speaking English in an American accent, off camera, choking with emotion.
"All shot and burned in their vehicle", she said, adding, "Only ashes and a few bones remain".
The video could not independently be verified.
The statement noted additional federal and local security forces were being sent into the area near the border between the two Mexican states, but did not provide further details.
The Intercept's Ryan Devereaux noted that the US has been helping Mexico wage a war on drugs for years-with disastrous consequences. The order was created as a Mormon offshoot in defiance of the church's prohibition on polygamy and has faced several controversies, including violence involving former leader Ervil LeBaron, who is accused of killing opponents.
The attack took place between Chihuahua and Sonora states.
Miller said the family was told that if the bullet had gone a quarter of an inch deeper into Brixon's chest, he would have been killed.The family is also anxious about 8-year-old Cody Langford, who was shot in the jaw."His jaw is actually broken".
Falko Ernst, senior analyst for the International Crisis Group in Mexico, said Trump's tweet suggests he may be gearing up to pressure Mexico over security, especially with his campaign under way for re-election in November 2020.