WASHINGTON—Two key lawmakers Wednesday circulated a proposal that would require companies to unlock encrypted technology when served with a court order, a notable change in the law that could escalate the clash between Silicon Valley and Washington.

Senate Intelligence Committee Chairman Richard Burr (R., N.C.) and the panel’s vice chairman, Sen. Dianne Feinstein (D., Calif.), are seeking input on proposed legislation that attempts to address one of the thorniest security issues vexing policy makers—how to deal with the use...