A police video displayed for the jury in Stephenville, Texas, showed officers in Lancaster, near Dallas, trying to coax Eddie Routh from a pick-up truck in the hours after famous US Navy SEAL Mr Kyle and his friend Chad Littlefield were found dead at a shooting range in February 2013.
Officers in the video were seen trying to talk Routh into surrendering as he made comments such as: “Anarchy has been killing the world.”
“He told us he’d taken a couple of souls and he had more souls to take,” Lieutenant Michael Smith of Lancaster police told the murder trial.
Defence lawyers have said Routh, 27, was insane when Mr Kyle, 38, and Mr Littlefield, 35, took him to a shooting range to provide support and camaraderie and said Routh believed the men planned to kill him. Routh faces life in prison without parole if convicted.
The case has drawn intense interest, largely because of Mr Kyle’s book American Sniper, about serving four tours in Iraq. The Oscar-nominated film based on the book has grossed nearly $300m (£196m).
Officers told the court that hours after the bodies were discovered, Routh returned to his home in Lancaster, driving Mr Kyle’s pick-up. Police spoke with him as he sat in the vehicle but he refused to leave, eventually speeding off with police in pursuit. He stopped minutes later after one police vehicle rammed the truck.
At one point, Routh wanted his parents to come. “There’s no trust anymore,” the video showed Routh saying.
At times, Routh made comments such as “I didn’t sleep a wink last night at all”, ‘’I don’t know if I’m going insane” and “Is this about Hell walking on Earth right now?”
Authorities say Routh had earlier driven to his sister’s house, admitted to the killings and told her “people were sucking his soul”.
Routh’s mother had asked Mr Kyle to help her son overcome personal troubles that twice led him to be admitted to a psychiatric hospital.
The trial continues.