Among them are 17 of the top 20 players in the current rankings including a host of Emirates Golf Federation invitees
"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.
"We don't agree (with Trump) on that," he told a news conference. "War is synonymous with irrationality."
"President Trump made clear that the United States condemns these senseless acts of violence that took the lives of nine American citizens and offered Mexico assistance to ensure the perpetrators face justice," said spokesman Hogan Gidley.
"It was a massacre," Julian LeBaron, an activist who has denounced criminal groups in the area, told Mexican radio network Formula.
He said the women were on their way to the airport with their children when their SUVs were attacked.
Several children managed to escape and return home on foot, he added.
Another, a three-month-old baby, was found wounded but alive beneath her mother's body.
An eight-year-old girl was also left missing for about 24 hours, before being found several kilometers away, unharmed.
Relatives said the children were all deeply traumatized. Five wounded children were airlifted for medical treatment in Phoenix, Arizona.
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. LeBaron, however, said the family believes they were deliberately attacked.
The LeBaron community are descendants of Mormons who fled the United States 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 the US network NBC.
Mitt Romney said on Twitter he was "heartbroken for the victims of the horrific attacks."
It is not the first time the LeBaron family has been targeted. Julian LeBaron's brother 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 United States needs to crack down on 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.
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