The dead included eight-month-old twins. Eight youngsters were found alive after escaping from the vehicles and hiding in the brush, but at least five had gunshot wounds or other injuries and were taken to Phoenix for treatment, officials said.

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.

Mexican Security Secretary Alfonso Durazo said the gunmen may have mistaken the group's large SUVs for those of rival gangs.

The bloodshed took place Monday in a remote, mountainous area in northern Mexico where the Sinaloa cartel has been engaged in a turf war. The victims had set out to visit relatives in Mexico, while one woman was headed to the airport in Phoenix to meet her husband.

"There's apparently a war right now," a relative of the dead who did not want his name used for fear of reprisals said wearily. "It's been going on for too long."

Around the ambush scene, which stretched for miles, investigators found over 200 shell casings, mostly from assault rifles.

In a tweet, President Donald Trump offered to help Mexico "wage WAR on the drug cartels and wipe them off the face of the earth".

But Mexican President Andres Manuel Lopez Obrador rejected that approach, saying his predecessors waged war, "and it didn't work".

The victims lived in Sonora state, about 110 kilometres south of Douglas, Arizona, in the hamlet of La Mora, which was founded decades ago by an offshoot of The Church of Jesus Christ of Latter-day Saints.

All of the victims were apparently related to the extended LeBaron family in Chihuahua, whose members have run afoul of the drug traffickers over the years. Benjamin LeBaron, an anti-crime activist who founded neighbourhood patrols against cartels, was killed in 2009.

Of the children who escaped, one had been shot in the face, another in the foot. One girl suffered gunshot wounds to her back and foot.

Cowering in the brush, one boy hid the other children and then walked back to La Mora to get help. Another girl, who was initially listed as missing, walked off in another direction, despite her gunshot wounds, to get help.

A group of male relatives set out to try to rescue the youngsters but turned back when they heard gunfire ahead.

The relative who did not want his name used said in an interview that when they finally made it to the scene where the ambush started, they found a burned-out Chevy Tahoe.

The gunmen had riddled the vehicle with dozens of bullets and apparently hit the gas tank, causing it to explode.

"When we were there, the cartels from Sonora, there were probably 50 or 60 of them, armed to the teeth, about a mile on this side," said the relative.

Trump tweeted that a "wonderful family" got "caught between two vicious drug cartels".

He said the US "stands ready, willing & able to get involved and do the job quickly and effectively," adding, "The cartels have become so large and powerful that you sometimes need an army to defeat an army!"

But Mexico's president said: "The worst thing you can have is war."

Later, the two leaders spoke by telephone, and Trump offered US assistance "to ensure the perpetrators face justice", the White House said without giving details.

Australian Associated Press