The man was also trying "to lure several children into his car," according to separate reports received by the department.
Local media reported there would be heightened security on Wednesday at the schools, which lock exterior doors during a "shelter-in-place" process, and that there had been no injuries.
Police arrested the 33-year-old man and recovered a loaded handgun after he was identified by a witness.
He was being booked into King County Jail for "numerous crimes," police said. (Reporting by Eric M. Johnson; Editing by Louise Ireland)