They say Devin Kelley, who shot dead 26 people at Sutherland Springs First Baptist Church and injured around 20 others, was not motivated by race or religious beliefs.
Wilson County Sheriff Joe Tackitt said Kelley, who opened fire during Sunday service at the small church, was motivated instead by personal circumstances.
He said Kelley had, prior to the attack, sent “threatening texts” to his mother-in-law, who was a member at the church but not present for the shooting.
A full statement issued by the Texas Department of Public Safety said: “There was a domestic situation going on within the family and the in-laws.
“The mother-in-law attended the church. We know he sent threatening, that she had received threatening text messages from him.”
And Republican Texas Governor Greg Abbott told CBS there was evidence that Kelley had mental health problems and that he had been denied a Texas gun permit.
He said: “It’s clear this is a person who had violent tendencies, who had some challenges, and someone who was a powder keg, seeming waiting to go off.”
Kelley, 26, had previously served in the US Air Force before being court-martialled and dishonourable discharged after assaulting his partner and her child.
His military dismissal means Kelley would not have been expected to have a gun licence. Despite this he sourced a Ruger .556 rifle, 9mm Glock handgun and a .22 Ruger, which were all found in his car after he fled the attack.
A spokesman for the Bureau of Alcohol, Tobacco, Firearms and Explosives said he should not have had guns.
He said: “In general, if an individual has a dishonourable discharge from the military, they would be prohibited from purchasing firearms.”
Kelley burst into First Baptist Church at around 11.20am local time wearing black tactical gear and holding a semi-automatic rifle.
He began firing at the church after parking across the road before entering and spraying the congregation with bullets.
When he left the building a nearby resident, who had heard the gunfire, shot at Kelley, who then fled.
The resident flagged down another car and he and the driver pursued the killer for up to seven minutes.
At this point Kelley, driving at high speed, lost control of his car and crashed it. Police quickly arrived at the scene and found the killer deceased with a self-inflicted gunshot wound.