With voter fury rising over the high cost of prescription drugs, Hillary Rodham Clinton proposed capping out-of-pocket drug expenses at $250 a month on Tuesday while a rival for the Democratic presidential nomination, Senator Bernie Sanders of Vermont, extolled his own plan and long record for pushing to lower drug costs.

While Republican candidates for the White House want to repeal the Affordable Care Act and generally oppose interfering with the drug industry, Mrs. Clinton and Mr. Sanders are competing fiercely with each other to press for greater competition and new regulations to rein in pharmaceutical companies. Mrs. Clinton announced her patient spending cap as part of a plan that includes requiring most drug makers to spend a defined portion of their profits on research and development, ending tax breaks for pharmaceutical advertising and allowing Americans to import lower-priced drugs from other countries.

“It has gotten to the point where people are being asked to pay not just hundreds but thousands of dollars for a single pill,” said Mrs. Clinton, who laid out her proposals at a forum in Iowa, where she and Mr. Sanders are running closely in opinion polls for the first-in-the-nation caucuses. “That is not the way the market is supposed to work. That is bad actors making a fortune off of people’s misfortune.”

Even before Mrs. Clinton spoke, Mr. Sanders issued a statement reiterating his proposals, made early this month, including letting people buy drugs from Canada and allowing Medicare to negotiate with drug companies over prices (which is also in her plan). He also noted that he has backed medication purchases from Canada since 1999, before Mrs. Clinton joined the Senate.