Mr. Kyle, author of the best selling book "American Sniper: The Autobiography of the Most Lethal Sniper in U.S. Military History," was with a struggling former soldier on just such an outing on Saturday, hoping that a day at a shooting range would bring some relief, said a friend, Travis Cox.

But the Texas authorities said Sunday that for unknown reasons, the man turned on Mr. Kyle and a second man, Chad Littlefield, shooting and killing both before fleeing in a pickup truck.  

"Chad and Chris had taken a veteran out to shoot to try to help him," Mr. Cox said. "And they were killed."

The police identified the gunman as Eddie Ray Routh, a 25-year-old veteran with a history of mental illness who had served in both Iraq and Afghanistan. The police offered no information about a possible motive.

Mr. Routh shot the men at about 3:30 p.m. on Saturday at the Rough Creek Lodge, an exclusive shooting range near Glen Rose, Tex., about 50 miles southwest of Fort Worth, Sgt. Lonny Haschel, a spokesman for the State Department of Public Safety's Highway Patrol Division, said in a statement. Mr. Routh was arrested on Saturday night at his home in Lancaster, a suburb south of Dallas. He has been charged with two counts of capital murder, Mr. Haschel said.

Mr. Cox, the director of a foundation that Mr. Kyle created, said he was not acquainted with Mr. Routh, but said that Mr. Kyle had devoted his life since his retirement from the military to helping fellow soldiers overcome post-traumatic stress.

In 2011, Mr. Kyle created the FITCO Cares Foundation to provide veterans with exercise equipment and counseling. He believed that exercise and the camaraderie of fellow veterans could help former soldiers ease into civilian life. "He served this country with extreme honor, but came home and was a servant leader in helping his brothers and sisters dealing with post-traumatic stress disorder," Mr. Cox, also a former military sniper, said by telephone.

Mr. Kyle, who lived outside of Dallas, had his own difficulties adjusting after retiring from the SEALs in 2009. He was deployed in Iraq during the worst years of the insurgency, perched in or on top of bombed-out apartment buildings with his .300 Winchester Magnum.

He became proficient at his job, racking up more than 150 kills and becoming a scourge of Iraqi insurgents, who put a price on his head and who were said to have nicknamed him the "Devil of Ramadi."

He preferred to think of his job not as killing bad guys, but saving the good.

"I feel pretty good because I am not just killing someone, I am also saving people," he said in a January 2012 interview with The Dallas Morning News. "What keeps me up at night is not the people that I have killed. It is the people I wasn't able to save."

Manny Fernandez contributed reporting.