George P. Bush in a letter called Kyle a "true American patriot," the Fort Worth Star-Telegram reported. The two men had arranged to go to a range together.
"I was immediately troubled by the irony of this tragedy -- that one of our greatest and most decorated Navy SEALs of our time, who fought so bravely for our country in multiple combat zones, was killed by one of our own, here at home," Bush said.
Kyle and a friend, Chad Littlefield, were killed Saturday at a gun range 80 miles from Fort Worth. The two men had taken Eddie Routh, a veteran allegedly suffering from post-traumatic stress disorder, to the range.
Bush, grandson of President George H.W. Bush and nephew of President George W. Bush, grew up in Florida but graduated from Rice University in Houston and the University of Texas law school. He lives in Fort Worth and is reportedly planning to seek political office next year.
In the letter, Bush, who served in Afghanistan as a Navy Reserve officer, said PTSD needs to be recognized.
"While certainly no excuse, the struggles for soldiers like the young man who took the lives of Chris and Chad are immeasurable," he said. "This was an unspeakable tragedy, but we must now look to the future and ask what we can do to prevent this from happening again."
Routh has been charged with two counts of capital murder.