The suspect died later Wednesday at Harborview Medical Center, hospital spokeswoman Susan Gregg said.
Police who began scouring the area for the person who opened fire at the cafe near the University of Washington responded a short time later to another fatal shooting near the city's downtown. They say a man killed a woman in an apparent carjacking and fled in a black SUV.
Police said late Wednesday they believe one man was responsible for both attacks.
"At this time, we feel pretty confident that we have the suspect," said Assistant Seattle Police Chief Nick Metz.
The Seattle Times identified the suspect as Ian Lee Stawicki, 40, of Seattle, citing unidentified law enforcement sources. Seattle police Sgt. Sean Whitcomb said he couldn't confirm the name and said police would not publicly identify the suspect Wednesday night.
Andrew Stawicki, 29, of Ellensburg, told the Times he recognized a photo shown on TV newscasts of the alleged gunman as his brother Ian. Andrew Stawicki said Ian Stawicki was mentally ill.
"It's no surprise to me this happened," he told the newspaper. "We could see this coming. Nothing good is going to come with that much anger inside of you."
A phone number for Andrew Stawicki rang busy when The Associated Press tried to reach him for comment.
The latest spasm of deadly gun violence to hit the city worried Seattle's leaders and prompted police to consider increasing patrols in high-crime areas. The five victims' deaths bring the number of homicides so far this year to 21, matching the total for all of last year.
Police said residents could expect a heightened police presence in the city for the time being.
Gunfire erupted late Wednesday morning at Cafe Racer, a restaurant and music venue north of the University of Washington. The gunman was described as a man, possibly in his 30s, wearing dark clothes.
Police released two photos from inside the cafe, apparently taken from a security camera. One shows a man walking into the establishment, with a woman nearby reading a book. Another photo shows stools overturned, and the man standing and holding what appears to be a handgun.
Two men died at the scene, and a third man and a woman from the cafe died at a hospital.
One man wounded in cafe shooting remained at Harborview in critical but stable condition following surgery earlier in the day. Gregg confirmed his name as Leonard Meuse. Meuse's father, Raymond Meuse, told the Times his son was shot in the jaw and armpit but was expected to survive.
A King County medical examiner's spokeswoman said her office might be able to release the dead victims' identifications Thursday.
Evan Hill, who lives above the building where the shooting happened, said the cafe was an artists' collective and performance space.
"It's the strangest place to think of a shooting," said Hill, who heard four to five shots. He said he ran to his balcony and called 911, but didn't see a suspect.
On a street corner across from the cafe, friends of the victims gathered by the ivy-covered wall of an apartment building. Some collapsed in grief. The cafe's owner hugged them and commiserated.
Units of police officers marched by with rifles and shotguns, knocking on doors and checking driveways and yards in the neighborhood of single-family, bungalow-style homes, restaurants and businesses.
In a narrative of the day's violence released Wednesday night, police said it appears the gunman fled to the First Hill neighborhood near downtown, where he fatally shot a woman in a parking lot and stole her SUV.
Police believe the gunman drove the SUV to West Seattle and ditched it, leaving a gun in the car. After officers found the vehicle, they flooded that area with uniformed and plainclothes officers.
Late Wednesday afternoon, a plainclothes detective spotted the cafe suspect and called for uniformed officers and a SWAT team, Assistant Police Chief Jim Pugel said.
As those officers arrived, the man put a gun to his head and pulled the trigger, Pugel said.
During the manhunt, Roosevelt High School, Eckstein Middle School and Greenlake Elementary were locked down, according to the school district.
In the last month, there have been two random killings in the city.
Last week, a man died when a stray bullet struck him as he and his family drove down a Seattle street. In late April, a woman died of injuries suffered in an apparently random drive-by shooting near downtown.
No arrests have been made in either of those fatalities.
On Saturday, a bystander was wounded near the Space Needle when he was struck by a bullet allegedly fired by a gang member involved in a dispute with another man, authorities said.
Later that night, about 60 shots were fired in drive-by shootings at four houses. No one was hit.
Besides the plan to increase the number of officers on patrol in high-crime areas, police are urging people with information about shootings to come forward.
At a news conference, Mayor Mike McGinn said the spate of violence had "shaken" the city.
"It's going to take our political leaders, coming together, to give our police officers the support and tools they need to do their jobs," McGinn said.
City Councilman Bruce Harrell said leaders needed to consider everything - from changing laws to addressing the culture of violence.
"If we are to be honest, there's no easy fix," he said.
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