He added that Sgt. Bowe Bergdahl had also forfeited his VA benefits for life with his dishonorable discharge for desertion and misbehavior before the enemy.
"In my opinion, I do not consider him a veteran," Shulkin said of alleged Texas shooter Devin Patrick Kelley.
"That would give him much more respect than he deserves," he said of Kelley, who served stateside in the Air Force until he was kicked out with a bad-conduct discharge for assaulting his wife and child.
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"He is a criminal," Shulkin said, and "does not deserve to have the same title as the men and women who have served this country and have honorably been discharged."
Law enforcement officials have charged that Kelley killed 26 churchgoers and injured at least 20 others Sunday when he opened fire outside and inside the First Baptist Church in Sutherland Springs, Texas, a small town about 30 miles east of San Antonio.
The officials said Kelley was found dead in his car of a self-inflicted gunshot wound after a high-speed chase by local residents.
Air Force officials said the 26-year-old Kelley joined the service in 2010 and served in logistics readiness at Holloman Air Force Base in New Mexico.
In wide-ranging remarks at the National Press Club, Shulkin said there is a distinction between those with bad-conduct and dishonorable discharges, and those with discharges under other than honorable conditions.
However, those with bad-conduct or dishonorable discharges do not deserve VA benefits or treatment, Shulkin said, "and the VA would not be providing those benefits."
He also appeared to take issue with President Donald Trump and Gov. Greg Abbott, R-Texas, who have said that Kelley was possibly mentally deranged.
In Japan on Monday on his Asian trip, Trump said the Texas shootings were a "mental health problem at the highest level," and not a "guns situation."
"I don't think we know enough about his state of mind to give him a diagnosis," Shulkin said. "Unfortunately, in this world, there are people that are evil and there are people that are criminal."
About Bergdahl, Shulkin said, "We would not recognize him as having the ability to receive benefits at VA. I don't believe he honors those who served and have worn the uniform proudly."
However, Shulkin said, as a doctor and "as a compassionate person, I certainly want him to get the help he needs and believe he should have access to treatment, but it would not be in the system that is supported by the Department of Veterans Affairs."
-- Richard Sisk can be reached at Richard.Sisk@Military.com.