The suspect is "a troubled veteran whom they were trying to help," said Craft International, a company founded by Kyle, who had tried to help veterans with PTSD since he retired from the Navy in 2009.

Routh, Kyle and his friend, Chad Littlefield, entered the resort and headed toward a gun range at 3:15 p.m. (4:15 p.m. ET) Saturday, according to authorities.

Marcus Luttrell told CNN that Kyle, his friend, had gone to help Routh get "out of the house (and) blow off some steam."

Around 5 p.m. Saturday, a hunting guide alerted authorities Kyle's and Littlefield's bodies had been discovered "lying on the ground, covered in blood," according to an affidavit for the search warrant for Routh's house.

By then, Routh allegedly had taken off in Kyle's black Ford pickup, stopping first at his sister's house about 70 miles away.

Gaines Blevins said his brother-in-law said "he'd traded his soul for a new truck and that he murdered two people," the affidavit says. "He said they were out shooting target practice and he couldn't trust them so he killed them before they could kill him. He said he couldn't trust anyone anymore; everyone was out to get him."

Laura Blevins told her brother that if what he was saying was true, "he needed to turn hisself in," it adds.

But Routh set off again.

At about 8 p.m., police caught up with him near his home in Lancaster, about 15 miles south of Dallas, and took him into custody.

The motive for the killings was unclear

Routh "is the only one that knows," Erath County Sheriff's Capt. Jason Upshaw told reporters on Sunday. "I don't know that we'll ever know."