Washington Gov. Jay Inslee encouraged residents and organizations to give “serious consideration” to canceling or postponing large events. He also directed state insurance providers to waive copays and deductibles for anyone qualified for testing for the virus, and directed the state’s labor department to ensure compensation for health-care workers and first responders who are quarantined.

“We are attempting to do everything humanly possible to slow the spread of this virus,” Mr. Inslee said.

North of Seattle, Northshore School District said it would close its 33 campuses for up to 14 days and that its students would continue their lessons online.

The decision, which officials said came after a parent at an elementary school tested positive for the virus, mirrors the actions of schools in Hong Kong, mainland China and Italy among other affected countries.