It was not clear whether the man, who police identified as Ian Stawicki, 40, of Seattle, was alive or dead after shooting himself in the head, ABC News reported.
"When the officers and SWAT started vectoring in on the suspect, the suspect saw uniformed officers, he apparently knelt down in the middle of the street and put the gun to his head," Seattle police Assistant Chief Jim Pugel told reporters.
Pugel said investigators "now feel confident in connecting" the shooting to the shooting death about 30 minutes later of a woman near Town Hall Seattle, The Seattle Times reported. ABC said police think the second shooting may have occurred during an attempted carjacking.
Stawicki's brother, Andrew Stawicki, 29, said Ian Stawicki was mentally ill and it was "no surprise to me this happened," the Times reported.
"We could see this coming," he said. "Nothing good is going to come with that much anger inside of you."
Deputy Chief Nick Metz said earlier he did not know the motive for the 11 a.m. PDT shooting at the Cafe Racer Espresso in the city's University District, but a law enforcement source told the Times it may have been related to a domestic dispute.
Two men were dead at the scene and Harborview Medical Center spokeswoman Susan Gregg said a woman died at the hospital. Two other men were in critical condition, she said.
A witness who said he used to work at the cafe told the Times the restaurant was generally quiet.
"They play folk music," he said. "Everybody is nice."
Doors were locked as a precaution on nearby elementary, middle and high schools, a school district spokeswoman said. Police later told the district it was safe for students to go home, she said.
The University of Washington, about 12 blocks from the shooting scene, alerted the campus community via social medial and e-mail but there was no lockdown, spokesman Norm Arkans said.