The town is located in the southern part of the state, about 35 to 40 miles from San Antonio.
The official said the gunman fled in a vehicle after the attack and was killed, either by a self-inflicted wound or during a confrontation with police.
US President Donald Trump on Sunday said that he was monitoring from Japan the shooting at a Baptist church in Texas.
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Abbot is en route to Sutherland Springs to speak with law enforcement and the victims. "I am monitoring the situation from Japan", Trump tweeted.
Texas Gov. Greg Abbott called the shooting an "evil act". "More details from DPS soon", Abbott tweeted.
Keeping all harmed in Sutherland Springs in our prayers and grateful for our courageous first responders on the scene. The first news reports of the shooting were between noon and 12:30 p.m.
There were "multiple fatalities and multiple wounded", according to Wilson County Commissioner Albert Gamez Jr, NBC News reported.
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The mass shooting comes just over a month after a gunman in Las Vegas fired down from a hotel room on a concert crowd, killing 58 people and wounding hundreds more.
The FBI is responding to the scene of the shooting, according to Michelle Lee, spokeswoman for the FBI's San Antonio field office. The FBI also was on the scene.
Witnesses said that the morning church service is usually attended by some 50 people. Weekly YouTube videos of the church's Sunday service don't show many more people than that in attendance.
Emergency officials are on scene and updated reports are expected.
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A sheriff's department dispatcher says everyone is at the scene and unavailable to comment.