Former Navy SEAL and American Sniper author Chris Kyle was fatally shot along with another man Saturday on a Texas gun range, police say.

Erath County Sheriff Tommy Bryant said Kyle and a second man were found dead at Rough Creek Lodge's shooting range west of Glen Rose, about 80 kilometres southwest of Fort Worth.

Sheriff's deputies responded to a call about a shooting at the lodge around 5:30 p.m., Sgt. Lonny Haschel said in a news release. Police found the bodies of Kyle, 38, and his neighbour Chad Littlefield, 35, at the shooting range.

Suspect, 25, charged

Witnesses told sheriff's investigators a gunman opened fire on the men around 3:30 p.m., then fled in a pickup truck belonging to one of the victims.

Police said the suspect arrived at his home in Lancaster, about 27 kilometres southeast of Dallas, around 8 p.m. Police arrested him after a brief pursuit and took him to the Lancaster Police Department.

Eddie Ray Routh, 25, of Lancaster was arraigned Saturday evening on two counts of capital murder, the Texas Department of Public Safety said Sunday.

The motive for the shooting was unclear.

There are unconfirmed reports that Kyle and Littlefield were helping a veteran with post-traumatic stress disorder when they were shot.

Kyle wrote the bestselling book, American Sniper: The Autobiography of the Most Lethal Sniper in U.S. Military History, detailing his 150-plus kills of insurgents from 1999 to 2009.

A news release from Travis Cox, director of FITCO Cares, a nonprofit Kyle helped start, said Kyle served four tours of duty in Iraq. Local media reports say he was wounded twice by gunfire.

"Chris died doing what he filled his heart with passion —- serving soldiers struggling with the fight to overcome PTSD," Cox said in the release. "He will be forever missed."

Kyle is survived by his wife, Taya, and their children, the nonprofit's release said.

He was sued by former Minnesota Gov. Jesse Ventura over a portion of the book that claims Kyle punched Ventura in a 2006 bar fight over unpatriotic remarks. Ventura says the punch never happened and that the claim by Kyle defamed him.

Kyle had asked that Ventura's claims of invasion of privacy and "unjust enrichment" be dismissed, saying there was no legal basis for them. But a federal judge said the lawsuit should proceed. Both sides were told to be ready for trial by Aug. 1.