Lieberman said discriminating against people with mental illness is "not the solution to violence in our country," but added that improving access to care for the mentally ill "would reduce these extremely rare but nevertheless tragic, senseless events."
Veterans have the option to seek treatment through Veterans Affairs hospitals, but Lieberman said many "fall through the cracks and never get connected to the help they need."
Several charities founded by veterans work to improve access to private mental health care, including FITCO Cares.
"It sounds like serviceman Kyle was among those trying to help his colleagues," Lieberman said. "That may be one of the cruelest ironies."
"This is a remarkable tragedy involving a true American hero who was reaching out, trying to help people of similar backgrounds, and it went terribly wrong," Everly said.
Kyle, author of the bestselling book "American Sniper: The Autobiography of the Most Lethal Sniper in U.S. Military History," leaves behind a wife and two children.
"We have lost more than we can replace," "American Sniper" co-author Scott McEwen said in a statement to ABC News. "Chris was a patriot, a great father, and a true supporter of this country and its ideals. This is a tragedy for all of us. I send my deepest prayers and thoughts to his wife and two children."