Some of the nine Mormon women and children massacred in Mexico were reportedly shot at point blank range.
The victims died while driving in Sonora, 80 miles south of the US border, where drug cartels have been fighting a turf war.
A US law enforcement official told the New York Post that, rather than dying in a hail of bullets, they had been “taken out of their cars and shot.”
And a Mexican official told the newspaper the attackers “shot some of the victims at point-blank range.”
Mexican authorities have said that the Mormon convoy drove into an ambush, and was hit by gunfire from high up in the hills surrounding the desert road.
They said hitmen may have mistaken the group’s large SUVs for those of a rival drug gang. General Hector Mendoza, Mexico’s army chief of staff, said it was “not a targeted attack”.
But the US official accused the FBI’s Mexican counterparts of trying to “cover everything up” and not wanting to investigate anything to do with drug trafficking.
The official told the New York Post: “It’s kind of disturbing that the FBI has had no access to the crime scene, which is probably a disaster already because the Mexicans have allowed families to remove the bodies.
“Any evidence that could have been gathered is probably destroyed.”
An FBI spokesman said: “We have offered assistance and stand ready to assist in the wake of this tragedy.”
The exact picture of what happened remained unclear after the last of the dead were buried on Saturday.
Some members of the offshoot Mormon community, based in the remote farming village of La Mora, decided to leave.
About 100 members arrived at the US border in an 18-vehicle convoy, mostly heading to stay with relatives in Phoenix and Tucson. Their trucks were loaded with boxes, bicycles, and other belongings.
Bryce Langford, whose mother was one of the women killed, told the Arizona Daily Star the community had learned more about cartel hit men operating in the area in recent months, and people had been considering moving before the massacre.
Mr Langford’s teenage brother hid half a dozen surviving children in bushes after the attack, and walked for six hours to get help.
He said: “We’re very proud of him. To be able to make those kind of decisions under those circumstances is something not a lot of people can say they can do.”