Seattle, Washington (CNN) -- A manhunt for a suspect in the shooting deaths of four police officers stretched into Monday night after the man appeared to have eluded authorities in an east Seattle neighborhood.

Maurice Clemmons, 37, is wanted in connection with what investigators called an ambush of the four officers from Lakewood, about 40 miles south of Seattle, on Sunday morning. Witnesses say Clemmons was shot during the attack, and police believe he is losing blood, Pierce County sheriff's spokesman Ed Troyer said.

Police surrounded a home in eastern Seattle's Leschi neighborhood for about 12 hours, but Clemmons was not found in the home when the siege was lifted Monday morning, Seattle police spokesman Jeff Kappel told reporters. Clemmons was believed to have been outside the home Sunday night, but apparently slipped out of the area, Kappel said.

His escape was "an unlucky thing for us, and a lucky thing for him," Troyer said Monday night.

"But his luck's going to run out, because he doesn't have people to help him do that any more," Troyer said.

Police have arrested several people they believe helped Clemmons flee, he said.

The killings took place at a coffee shop in Parkland, a suburb of Tacoma. Authorities identified the victims as Sgt. Mark Renninger, 39; Officer Ronald Owens, 37; Officer Tina Griswold, 40; and Officer Greg Richards, 42.

Early Monday, authorities started identifying Clemmons as a suspect, rather than as someone wanted for questioning.

The night before the shootings, Clemmons threatened to kill police officers, but witnesses did not report those threats until after the slayings, Troyer said on "Good Morning America."

Clemmons is a convicted criminal with a long rap sheet in Washington and Arkansas, according to authorities and documents. He was accused of child rape and assaulting a police officer in May, and was released on $150,000 bond five days before the shootings, according to court records.

After his arrest, Clemmons' sister told police that he "had not been himself lately" and that his behavior was "unpredictable and erratic."

"He had said that the Secret Service was coming to get him because he had written a letter to the president," an affidavit quoted her as telling investigators.

In addition, neighbors complained he threw rocks through their windows. Clemmons' wife told deputies that she and her husband argued over a "newly discovered child," and she suggested that was why he went on his rock-throwing spree, according to an arrest affidavit.

Clemmons was given a 95-year prison sentence in Arkansas in 1989 for a host of charges, including robbery, burglary, theft and bringing a gun to school. His sentence was commuted in 2000 by then-Arkansas Gov. Mike Huckabee, Troyer said.

Read the documents for Clemmons' clemency

Clemmons returned to prison in 2001, but was paroled in 2004.

"Should he be found responsible for this horrible tragedy, it will be the result of a series of failures in the criminal justice system in both Arkansas and Washington state," Huckabee's office said in a statement Sunday night.

During his 2008 presidential bid, Huckabee was criticized for granting clemency to another inmate, convicted rapist Wayne DuMond, who was later convicted of raping and murdering a woman in Missouri. Huckabee's statement brought a sharp response from Troyer on Monday.

"We're disappointed that Gov. Huckabee came out in the middle of the night without calling anybody here and blamed this on the criminal justice system in the state of Washington," Troyer said. "We're guessing that's probably a spin doctor, not him."

Sunday's shooting was the first for the Lakewood Police Department, which was created five years ago for the town of nearly 60,000. Until then, the Pierce County sheriff's office provided law-enforcement services there.

Police Chief Bret Farrar told reporters Monday he has repeatedly been asked how the city's officers are doing.

"This is how everybody's doing," Farrar said, gesturing to the police force standing behind him. "They're here. They're doing their jobs. They're working hard. They're dealing with their loss. ... We're here to carry on. This is what we do."

The four officers "were good people," Farrar said, fighting to maintain his composure. "They were great officers, and we will all miss them very much."

The Lakewood Independent Police Guild is accepting donations for the officers' families, said guild president and Lakewood police officer Brian Wurts. Contributions have come from as far away as Switzerland, he said.

"I can't believe he was out on the street," Wurts said of the suspect. "You have 5 percent of the people out here committing 90 percent of the crime -- not against just us, but against all of you. And we've got to hold these people accountable. We've got to keep them locked up. And if they want to rehabilitate them, you can rehabilitate them, but you rehabilitate them in prison, where they're supposed to be. This guy should have never been on the street."

The coffee shop on Steele Street is a popular hangout for law enforcement officers and is one of 22 Forza Coffee Co. locations in Washington.

"As a retired police officer, this senseless shooting hits extremely close to home to me," Brad Carpenter, chief executive officer of Forza, said in a statement on the company's Web site.

Police said there was no warning. The shooter walked past the officers to the counter as if to order coffee before he pulled a gun out of his coat and began shooting at 8:15 a.m. Sunday, Troyer said.

Two of the officers were "executed" as they sat at a table, said Troyer, the sheriff's spokesman.

Another was shot when he stood up and the fourth was shot after struggling with the gunman all the way out the door, Troyer said. All were in uniform, with their marked patrol cars parked outside.

Two coffee shop employees and other customers inside the shop were unharmed. "Just the law enforcement officers were targeted," Troyer said.

"After, we believe, some of the officers were shot, one of them managed to fight his way with the suspect -- fight his way, wrestle, fight all the way out the doorway until he was shot and died of a gunshot wound," he told reporters.

Griswold' sister, Tiffany Ryan, told reporters her "worst nightmare has come true."

"I can't tell you how painful it is to lose my sister," she said. "If that man is watching this ... I want him to know what he took from us. I won't ever get to see her again. She won't ever get to watch her children grow and her daughter get married and have children."

CNN's Patrick Oppmann, Peter Hamby, Dave Alsup and Dina Majoli contributed to this report.