Investigators have established a "person of interest" with an extensive criminal background in the ambush shooting deaths of four police officers in a Washington-state coffee shop.

Pierce County sheriff's spokesman Ed Troyer told reporters that Maurice Clemmons, 37, is one of several people police want to talk to but refrained from calling him a suspect.

Clemmons has an extensive violent criminal history in Arkansas, including aggravated robbery, according to a police news release. He recently was arrested and charged in Pierce County for third-degree assault on a police officer, and second-degree rape of a child.

The four Lakewood Police Department officers, three men and one woman, were seated in the cafe and working on laptops when a gunman entered the Forza Coffee Co. and shot them Sunday morning at about 8:15 a.m.

The slain officers have been identified as: 39-year-old Sgt. Mark Renninger, 37-year-old Ronald Owens, 40-year-old Tina Griswald and 42-year-old Greg Richards.

Two were shot while they were still sitting down in the shop, and a third was killed after standing up. The fourth struggled with the gunman at the doorway and put up "a good fight," firing off a few shots before succumbing to his wounds.

"We believe there was a struggle, a commotion, a fight ... that he fought the guy all the way out the door," Troyer said. "We hope that he hit him."

Troyer said that police are asking medical providers to report anyone wounded by gunshots.

The suspect fled on foot. No one else in the cafe was injured.

Troyer said it was not a robbery, and the officers appeared to have been targeted in the attack.

"This was more of an execution. Walk in with the specific mindset to shoot police officers," Troyer said. "There were marked patrol cars outside and they were all in uniform."

Police described one suspect as a black male, about 5'9 and in his 20s or 30s. He was unshaven, wore a black coat and blue jeans. They believe he used a handgun.

"Anybody that would go in and (shoot the officers) is definitely somebody who's dangerous, and knows we're going to be looking for him," Troyer told CTV News Channel early Sunday evening.

Authorities may also be looking for a second suspect in the case, although no description has been released.

The coffee shop is located near an Air Force base in a commercial area, about 55 kilometres south of Seattle.

Roads have been closed around the site of the attack as police investigate.

Toyer said a US$10,000 reward has been offered for information about the shooting.