A man and a woman were found dead in separate apartments during a search of the building in Federal Way.
One man lying injured in a car park died from gunfire after producing a weapon when police approached him, though it is not clear whether he was killed by a police bullet.
Two other men were found dead in the complex grounds.
“When we arrived, there was a lot of gunfire already being fired and multiple calls, 911 calls of gunfire,” Federal Way police spokeswoman Cathy Schrock said.
It is not clear how the shooting incident at the complex began, but local television quotes police as saying it was a firefight between the four men who died.
“We’re going to continue to go door to door in hopes that we can find some additional witnesses, and hopefully we won’t be finding any more victims,” Ms Schrock told AP.
Police carried out extensive searches but said they did not think there were any more gunmen at large in the district.
Federal Way is about 20 miles (32km) south of Seattle.
-Agencies
