Governor Jay Inslee said Mr Trump should stay out of the state's business, and Seattle's mayor said any invasion of the city would be illegal.
Police abandoned a precinct there on Monday after days of clashes.
Mr Trump said the area had been overtaken by "domestic terrorists".
Since police withdrew, demonstrations in the area have been largely peaceful.
It has been called Chaz, an abbreviation of Capitol Hill Autonomous Zone. Hundreds of people have been gathering there to demonstrate, hear speeches and attend events.
The protests in Seattle, Washington began in response to last month's death in police custody of an unarmed black man, George Floyd, in Minneapolis, Minnesota.
President Trump, who has pushed states to take firm action against protesters, has meanwhile outlined proposals for reforming police, including greater funding for training and national guidelines on the use of force.
However, he dismissed calls for defunding the police as an "extreme agenda". Such a measure involves budgets being allocated directly to communities rather than law enforcement.