Mexico City — At least nine U.S. citizens, including six children, who lived in a Mormon community in northern Mexico were killed Monday in a hail of gunfire, according to family members and Mexican officials. A source told CBS News one theory is that the group was intentionally targeted. Supporting that scenario, the ambush was not short and was spread out for miles.

Another scenario, other investigators said, is that the family was caught in the middle of a battle between two rival drug gangs. The Mexican government has spoken about this scenario.

Family members told "CBS This Morning" that the FBI has opened an investigation into the killings. It happened Monday near the town of Bavispe, about 100 miles south of the Arizona border. The victims all left their community at the same time in three separate cars, some were traveling back to the U.S., some to a neighboring town for a wedding.

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Suddenly, the convoy of SUVs was sprayed with gunfire. There were so many rounds that family members said one of the cars exploded.

The families are members of the La Mora settlement, a decades-old community in Sonora state founded as an offshoot of The Church of Jesus Christ of Latter-day Saints.

One relative said he located one of the burned-out, bullet-ridden SUVs containing the remains of his nephew's wife and her four children, twin 7-month-old babies and two other children aged 8 and 10.

U.S. Ambassador to Mexico Christopher Landau said in a tweet that Mexican authorities had informed their U.S. counterparts that the dead included three women and six children.

Jhon LeBaron, one of the relatives, posted on his Facebook page that his aunt and another woman were dead. He said six of his aunt's children had been left abandoned but alive on a roadside. He wrote late Monday that a total of 17 of his family members were in the three-vehicle convoy when it came under attack. He said nine were killed, six wounded, and two left unharmed.

Another relative, Julian LeBaron, identified one of the slain adults on his Facebook page as Rhonita Maria LeBaron. Jhon identified her as Maria Ronita LeBaron. She was apparently killed along with her twin seven-month-old babies and two of her other seven children.

The first relative said the convoy set out Monday from La Mora, about 70 miles south of Douglas, Arizona, but was attacked by cartel gunmen in a possible case of mistaken identity. Many of the church's members were born in Mexico and thus have dual citizenship.

A burned-out SUV is seen parked by the side of a remote road in northern Mexico's Sonora state on November 4, 2019. Reuters

Video emerged showing the still-smoldering remains of one SUV ditched along a road in a remote area. The inside of the vehicle was completely burned out.

Trish Cloes is victim Dawna Ray Langford's aunt. She said the family was devastated and emotional and all they could do was "start thinking positive and praying" when they heard about the tragedy.

"It's something that you can't explain, that there are evil people in this world that could do such a thing like that," she said.

Cloes said she wanted people to remember her relatives as "amazing, family-oriented people. They are loving, they are giving… they're always looking out for others."

It would not be the first time that members of the break-away church had been attacked in northern Mexico, where their forebears settled — often in Chihuahua state — decades ago. In 2009, Benjamin LeBaron, an anti-crime activist who was related to those killed in Monday's attack, was murdered in neighboring Chihuahua state.

Trump offers to wage "war" on cartels

A wonderful family and friends from Utah got caught between two vicious drug cartels, who were shooting at each other, with the result being many great American people killed, including young children, and some missing. If Mexico needs or requests help in cleaning out these..... — Donald J. Trump (@realDonaldTrump) November 5, 2019

President Trump appeared to confirm in a series of tweets on Tuesday morning that it was cartel gunmen behind the attack on the family convoy. He said the family "got caught between two vicious drug cartels, who were shooting at each other."

"If Mexico needs or requests help in cleaning out these monsters, the United States stands ready, willing & able to get involved and do the job quickly and effectively," Mr. Trump said. "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. We merely await a call from your great new president!"

Senator Mike Lee, a Republican from Utah, said later Tuesday that the U.S. government was "still getting the details" of the case, and it remained unclear "whether these individuals were singled out or whether they happen to be at the wrong place at the wrong time."

During a live news conference alongside one of his senior security officials, Mexican President Andres Manuel Lopez Obrador said Tuesday that he did not believe his country would "need foreign intervention to deal with such cases," but that he was prepared to allow Mexican authorities to work with their U.S. counterparts, provided Mexico's independence was respected.

"I haven't yet seen the message" from Mr. Trump, Lopez Obrador said, adding that he was confident it was meant as an offer to cooperate and help, "and we respect this a lot."

But Lopez Obrador rejected Mr. Trump's call for a "war" with the cartels. "The worst that we could see is war," he said. "I always say politics was invented to avoid war... War is irrational. We are for peace. It is a characteristic of this new government."

Mexico's federal Department of Security and Citizens' Protection said security forces were reinforced with National Guard, army and state police troops in the area following "the reports about disappearance and aggression against several people."

Andy Triay contributed to this report.