The four Lakewood, Wash., police officers who were shot to death Sunday in a suburban coffee shop are, from left: Greg Richards, 42, Tina Griswold, 40, Ronald Owens, 37, and Mark Renninger, 39. (City of Lakewood/Associated Press)

Seattle police have fatally shot a man who was sought in the killing of four police officers on Sunday.

Maurice Clemmons, 37, was shot at about 2:45 a.m. local time Tuesday in a south Seattle neighbourhood.

Assistant police chief Jim Pugel said a police officer was investigating a stolen car when he detected movement behind him, recognized Clemmons and ordered him to put his hands up.

"He wouldn't stop," Pugel said. "The officer fired several rounds, took the person into custody."

Clemmons already had a serious gunshot wound from Sunday, when he was hit by a bullet from one of the four police officers he killed.

Clemmons has since died from his wounds, Pugel said. He said Clemmons had been carrying a handgun taken from one of the slain police officers.

The four officers — three men and one woman — were about to start their day shift in a community near Tacoma, south of Seattle, and were sitting at laptop computers in a Forza Coffee Co. shop when a man entered and opened fire on them with a handgun, officials said.

Police had been hunting for Maurice Clemmons, 37, in connection with the killing of the four police officers. They said early Tuesday that he had been fatally shot. (Pierce County Sheriff's Department/Associated Press)

The slain officers were identified as Greg Richards, 42, Tina Griswold, 40, Ronald Owens, 37, and Sgt. Mark Renninger, 39.

Pierce County sheriff's department spokesman Ed Troyer said Seattle police found Clemmons after being supplied by county authorities with addresses of possible hiding spots.

Troyer said four other people have been arrested on allegations they helped Clemmons elude authorities. He said police expect to arrest up to seven people by the end of the day.

"Some are friends, some are acquaintances, some are partners in crime, some are relatives. Now they're all partners in crime," Troyer said.

Police have said they don't know what prompted the gunman to shoot the officers while sparing employees and other customers in the shop.

Troyer previously stated that Clemmons "made comments the night before to people that he was going to shoot police and watch the news."

Clemmons's criminal record includes a 95-year prison sentence for robbery, imposed in 1989, that was commuted by former Arkansas governor Mike Huckabee in 2000.

He was recently arrested on allegations he assaulted a police officer in Washington state and was released from jail last week after a $150,000 US bond was posted by a bail bondsman.

In a statement posted on his website Sunday, Huckabee pointed the blame at the justice system.