Bryant said Routh has an attorney but hasn't met with him at the jail in Stephenville, about 75 miles southwest of Fort Worth.
Attempts by The Associated Press to reach Routh's mother and sister were unsuccessful Monday.
Sundae Hughes, an aunt of Routh's, said she watched him grow up but hasn't seen him since his high school graduation in 2006. Hughes was in disbelief that her nephew could be involved in such an incident.
"He has a kind heart (and was) someone willing to jump in and help, no matter what it was," she said.
Routh joined the Marines in 2006 and rose to the rank of corporal in 2010. His military specialty was small-arms technician, commonly known as an armorer. He had been stationed at Camp Lejeune, N.C., and served in Iraq from 2007-08 and in the Haiti disaster relief mission in 2010.
He is now in the individual ready reserve. He could be called to duty, but it's uncommon unless he volunteers, 1st Lt. Dominic Pitrone of the Marine Forces Services public affairs office said.
Travis Cox, director of FITCO Cares — the nonprofit that Kyle set up to give in-home fitness equipment to physically and emotionally wounded veterans — said he believes that Kyle and Littlefield were helping Routh work through PTSD.
Cox didn't know how Routh and Kyle knew each other. He said the shooting range event was not a FITCO session.
Kyle, 38, left the Navy in 2009 after four tours of duty in Iraq, where he earned a reputation as one of the military's most lethal snipers. "American Sniper" was the No. 3 seller of paperbacks and hardcovers on Amazon as of Monday, and the hardcover was out of stock.
Littlefield, 35, was Kyle's friend, neighbor and "workout buddy," and also volunteered his time to work with veterans, Cox said.
Stengle reported from Midlothian, Texas. Associated Press writers Juan Carlos Llorca in El Paso, Texas; Christopher Sherman in McAllen, Texas; Martha Waggoner in Raleigh, N.C.; and AP researcher Rhonda Shafner contributed to this report.