A suburban Seattle school district launched the farthest-reaching school closures in the U.S. Thursday in an attempt to contain the coronavirus, directing more than 23,500 students to stay home for up to two weeks in a last-resort step that districts across the country are considering.

The number of deaths in Washington state rose to 11 Thursday and confirmed cases jumped to 70 from 39 a day earlier, prompting companies including Microsoft Corp., Amazon Inc. and Facebook Inc. to encourage employees in the region to work from...