Chuck Young, the park’s chief ranger, said Mr. Barnes was found about a mile or a mile and a half from Barn Flat, a bend in a park road where officials say he shot and killed the ranger, Margaret Anderson, 34, after she tried to stop his vehicle.

Mr. Barnes had failed to stop when park rangers tried to pull him over Sunday morning. Ms. Anderson, responding to radio calls, used her patrol vehicle to create a blockade as Mr. Barnes made his way toward the busy Paradise visitor center and recreational area, where fresh snow had lured people to go sledding and snowshoeing. The gunman is believed to have stepped out of his vehicle and shot Ms. Anderson before she could react.

“There’s nothing she could have done,” Mr. Troyer said.

Ms. Anderson had two daughters, ages 3 and 1, and was married to another ranger at the park. She joined the Park Service as a seasonal ranger at Bryce Canyon National Park in Utah in 2000. The couple had worked at Mount Rainier since 2008.

No one else was injured, though Mr. Barnes is believed to have shot out the windshield of another ranger who responded.