Matthew Ryan Buquet appeared in U.S. District Court in Spokane after his Wednesday afternoon arrest, KHQ-TV, Spokane, reported.
The letters were postmarked last week in Spokane and addressed to a federal building and the post office in downtown Spokane. They were intercepted by the U.S. Postal Service, and no one was hurt, the TV station said.
Buquet could face 10 years in prison if convicted of mailing a threatening communication.
A bail hearing was set for Tuesday.