By Laura L. Myers

SEATTLE (Reuters) - A gunman shot three people to death at a popular Seattle cafe on Wednesday then fled to a downtown parking lot where he killed another woman and stole her car before shooting himself in the head as police closed in, authorities said.

The man, who was not immediately identified, was being treated at Harborview Medical Center following the late-morning spree, which police initially treated as separate incidents.

The burst of gun violence prompted a security alert and lockdown at several Seattle schools and city-run community centers in north Seattle, where residents were advised to stay behind closed doors as police searched for the suspect.

Seattle Mayor Mike McGinn told a news conference that the two slayings, following a recent rash of other shootings, had shaken the city. He urged municipal leaders to "bring an end to this gun violence that the city is seeing."

Authorities had no immediate explanation for the bloodshed, which they said began when the gunman opened fire at the Cafe Racer, an establishment in Seattle's Ravenna neighborhood known for its live music.

Two men were killed outright, and three other people struck by gunfire were taken to Harborview, where one of them, a woman, died of her wounds.

None of the victims was immediately identified, but local television station KIRO7 reported that some of them may have been musicians.

Police said the suspect fled on foot and made his way a short time later to downtown Seattle, where he shot another woman dead and drove away with her sport utility vehicle.

Police later found an SUV matching the description of the getaway vehicle, with a handgun visible inside, in a West Seattle neighborhood.

The suspect was gone, but officers who confronted him a short time later saw him kneel down and shoot himself in the head, police said.

"The man detectives believe to be the lone suspect in 4 murders in 2 locations shot himself in the head when approached" by Seattle police, the police department said in a statement posted on Twitter.

(Additional reporting by Dan Whitcomb, Mary Slosson. Writing by Steve Gorman; Editing by Cynthia Johnston and Christopher Wilson)