The shooting ended quickly when armed parishioners fired back, killing the shooter.
Investigators said the shooter, wearing a dark hooded sweatshirt, was among the 240 congregants at West Freeway Church of Christ in White Settlement, a city 10 miles west of Fort Worth.
During the service, he stood up from a back pew, pulled out a shotgun, and began firing. Two church members, identified Monday as 64-year-old Anton Wallace and 67-year-old Richard White, were shot and later died in the hospital.
Within six seconds, a member of the church's security team was able to subdue the attacker, killing him.
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FBI Special Agent in Charge Matthew DeSarno said Kinnunen is "relatively transient" but had roots in the area.
Sources also said Kinnunen had been arrested multiple times in the past: in 2009 in River Oaks, Texas, for unpaid traffic tickets and then again in 2016 in Linden, New Jersey, for unlawful possession of a weapon.
He also has a warrant from Tarrant County for possession of narcotics in 2009.
The FBI is working to identify the gunman's motive.
The suspect's sister, Amy Kinnunen, told ABC News her brother was the shooter and emphasized that he had a difficult childhood. She said Sunday was the birthday of their brother Joel Kinnunen, who died 10 years ago by suicide.
Video of the shooting, which was recorded on the church's livestream, shows people panicking. One man was seen shielding his wife with his own body.
At least five others in the church pulled out handguns and carefully approached the fallen gunman.
"It was a sad thing that he had to come into the congregation and hurt people, and it's a sad thing that we had to hurt him," a parishioner said.
Tiffany Wallace told Dallas TV station KXAS that her father, "Tony" Wallace, was one of the victims killed in the attack. She said her father was a deacon at the church and had just passed out communion when the gunman approached him.
"I ran toward my dad, and the last thing I remember is him asking for oxygen, and I was just holding him, telling him I loved him and that he was going to make it," Wallace said.
At a press conference Sunday night, Texas Lt. Gov. Dan Patrick hailed the state's gun laws, including a measure enacted earlier this year that allowed licensed guns in places of worship, unless the facility bans them.
"Two of the parishioners who were volunteers of the security force drew their weapons and took out the killer immediately, saving untold number of lives," Patrick said.
WATCH: Authorities praise church security volunteers for stopping gunman
Britt Farmer, senior minister of the church, said, "We lost two great men today, but it could have been a lot worse."
Sunday's shooting was the second attack on a religious gathering in the U.S. in less than 24 hours. On Saturday night, a man stabbed five people as they celebrated Hanukkah in an Orthodox Jewish community north of New York City.
The Associated Press contributed to this report.