WASHINGTON—Senate Intelligence Committee Chairman Richard Burr (R., N.C.) has decided against a proposal circulating quietly on Capitol Hill to create criminal penalties for companies that decline to comply with court orders to decipher encrypted communications, a spokeswoman said Thursday night.

The issue of how to pressure companies on encryption matters has become inflamed in Washington in recent days. Several people familiar with the matter previously said Mr. Burr was considering criminal provisions as part of the proposal....