The victims are members of the LeBaron family, linked to a breakaway Mormon community which settled in Mexico several decades ago.
The victims, who also include three women, were travelling in a convoy.
Mexico's security minister said the group could have been targeted accidentally through mistaken identity.
Family members, who have spoken to the New York Times newspaper, said two of the children killed were less than a year old.
In a Tuesday-morning tweet President Donald Trump described the group as "a wonderful family and friends" who "got caught between 'two vicious cartels'".
In a series of posts, he signalled that the US "stands ready" to offer support to combat the problem.
As news of the attack spread, the death toll was at first unclear.
However, family members and Mexican officials have now confirmed that at least nine people were killed.
LeBaron family members were quoted as saying a group of three mothers and their 14 children had set off in a convoy of cars from Bavispe in Sonora state and were heading to La Mora in the neighbouring state of Chihuahua.
They were ambushed by gunmen in Bavispe.
A burnt-out SUV was later found by the side of the road with the remains of some victims and there were reports that other family members were shot at as they tried to flee.
Julian LeBaron, a cousin of the three women, also said seven other children managed to escape the attack.
The attack is thought to be have been carried out by a drug cartel which operates between the two states.
The governments of Chihuahua and Sonora issued a joint statement saying that an investigation had been launched and additional security forces had been sent to the area.
Claudia Pavlovich Arellano, governor of the state of Sonora, described the perpetrators on Twitter as "monsters".
"As a mother, I feel anger, revulsion and a profound pain for the cowardly acts in the mountains between Sonora and Chihuahua," she wrote, in Spanish.
Who are the victims?
Twins under the age of one were among the dead, the family said. The other child victims were aged 11, nine, six and four.
The victims are members of a community called Colonia LeBaron which was founded by a breakaway Mormon group in the first half of the 20th Century after the Church of Jesus Christ of Latter-day Saints in the US starting cracking down on polygamy.
The community now includes both Mormons and Catholics who have settled there. Members are known for standing up to local drug gangs and speaking out about the high levels of cartel violence.
Possible international repercussions
Even by the standards of Mexico's drug war this was a particularly horrific attack.
A video reportedly filmed and posted online by a distraught family member shows a completely burnt-out car on a hillside, said to be on the road to La Mora.
The violent ambush is likely to have international repercussions too, as many of those killed were US citizens.
Mexican President Andrés Manuel López Obrador has said he is employing a policy of non-violence and non-confrontation with the powerful cartels, but his critics accuse him of lacking any kind of coherent security strategy.
Pressure is growing on the government after an embarrassing episode last month when the police in Sinaloa released the son of the jailed drug lord, El Chapo Guzmán, after they were outgunned by his men.
While local media say the convoy of cars may have been mistaken for that of a rival gang, the LeBaron community has been targeted by the cartels in the past. In 2009, Erick LeBaron was kidnapped for ransom. The community took a stand and said it would not pay for his release as that would just encourage future kidnappings.
Erick LeBaron was eventually released without a ransom being paid. But months later, his brother Benjamin, who had led the campaign for Erick's LeBaron's release, was beaten to death. Benjamin's brother-in-law was also killed.
In 2010, Julian LeBaron published an article in the Dallas Morning News calling for Mexicans to stand up against organised crime.
The Colonia LeBaron community has in the past demanded to be allowed to create its own security force.
This area of northern Mexico is being fought over by two rival gangs, La Línea, which has links to the larger Juárez cartel, and "Los Chapos", which is part of the Sinaloa cartel.
The power and influence of the Sinaloa cartel was on display last month when its members barricaded streets and clashed with security forces in Culiacán after one of their leaders, Ovidio Guzmán López, was arrested.
With the security forces outnumbered and surrounded, the Mexican government took the controversial decision to free Ovidio Guzmán to prevent further bloodshed.
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