U.S. presidential candidate Bernie Sanders and a fellow lawmaker are taking aim at high prescription drug costs with a new bill that would empower Medicare to negotiate pharmaceutical prices, allow consumers to import cheaper drugs from Canada and require companies to disclose the prices they charge overseas.

Sen. Sanders, the Vermont independent running for the Democratic Party’s presidential nomination, and Rep. Elijah Cummings, a Democrat from Maryland, plan to introduce the Prescription Drug Affordability Act of 2015 at...