Gunmen ambushed the members of the LeBaron family -- a large clan of Mormons who emigrated to Mexico in the late 19th century -- as they traveled on a rural road Monday in a lawless region between the border states of Sonora and Chihuahua.
Mexican officials said six children were wounded and another girl missing after the attack, which left the family's three cars riddled with bullets and utterly charred, as seen in images posted on social media by devastated relatives, Presstv Reported.
"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," Trump wrote in a tweet.
He praised Mexican President Andres Manuel Lopez Obrador for prioritizing the fight against drug trafficking, but said "the cartels have become so large and powerful that you sometimes need an army to defeat an army!"
"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!"
Lopez Obrador said he would call Trump and accept "all necessary cooperation."
But the left-wing populist, who has declared an end to Mexico's "drug wars," said he was not looking for a new one.
"We don't agree (with Trump) on that. We respect those who think that way, but it goes against our convictions. War is the worst thing there is," he told a news conference.
"War is synonymous with irrationality."
Shocked, outraged members of the LeBaron family took to social media to call for people's prayers and condemn the lawless violence gripping much of the border region.
The victims "were ambushed by the Mexican cartels; shot, burned, and murdered in cold blood. These were innocent civilians," said one.
"It was a massacre," Julian LeBaron, an activist who has denounced criminal groups in the area, told Mexican radio network Formula.
His said the three women were on their way to the airport with their children when their SUVs were attacked.
At least five children managed to escape and walk home, he added.
Mexican Security Minister Alfonso Durazo said the family may have been mistakenly targeted or caught in the crossfire in turf wars between rival drug cartels.
The LeBarons's community are descendants of Mormons who fled the US in the late 1800s after being persecuted for their traditions, including polygamy. Many are dual US-Mexican citizens.
One former member is George Romney, father of 2012 Republican presidential candidate Mitt Romney, who was born in 1907 in Colonia Dublan in Chihuahua state, according to NBC.
Romney said on Twitter he was "heartbroken for the victims of the horrific attacks."
It is not the first time the family has been targeted. Julian LeBaron's sibling, Benjamin, founder of a crime-fighting group called SOS Chihuahua, was assassinated in 2009 after he led protests over the kidnapping of their 16-year-old brother.
The murder came after the Mormons refused to pay the ransom. The young LeBaron was eventually released.
The region around the 3,145-kilometer (1,954-mile) US-Mexican border is plagued by violent crime.
Trump, who is battling to build the border wall that was his signature campaign pledge, regularly tells Mexico to do more to fight drug trafficking and illegal migration across the frontier.
Lopez Obrador typically responds that the US needs to do more to fight illegal firearms trafficking, which generates an estimated $127 million in profits a year for the American gun industry.
Mexico has registered more than 250,000 murders since the government controversially deployed the army to fight drug trafficking in 2006.
Many experts blame the "drug wars" for spiraling violence, as fragmented cartels battle each other and the army.
Lopez Obrador has struggled to rein in the violence since taking office in December 2018. This year appears on track to set a new murder record in Mexico, with 25,890 so far.