Rep. Elijah Cummings (D-Md.), ranking member on the House Benghazi Committee, speaks on Capitol Hill in Washington on Oct. 22,  where former secretary of state Hillary Rodham Clinton testified. (Carolyn Kaster/AP)

Democrats on the House Oversight Committee are chastising Chairman Jason Chaffetz (R-Utah) for rebuffing their efforts to investigate price hikes by two pharmaceutical companies.

"My constituents are dying," Ranking Member Elijah E. Cummings (D-Md.) said at a news conference Wednesday morning. "They are dying because they cannot get a cure."

In a letter to Chaffetz, he and other members said Republicans have "refused every request" to hold hearings or issue subpoenas to drug companies. They ask Republicans to allow them to move forward next month: "Even if you have no interest in investigating these abuses on behalf of your own constituents, we ask that you not block us from investigating them on behalf of ours."

Cummings has for months been urging an investigation into Valeant Pharmaceuticals, which is now being probed by federal prosecutors, and has demanded documents from both Valeant and Turing Pharmaceuticals. After those requests were refused, he and his fellow Democrats in September pushed for hearings where the CEOs of the two firms would testify.

He said Wednesday that three Republicans, including one member of the Oversight Committee, have asked him to push Democrats to do something about drug prices.

"I say talk to Chaffetz," he said. He added that he hoped newly-elected House Speaker Paul D. Ryan (R-Wis.) will take up the issue.

A spokeswoman for Chaffetz did not immediately return a request for comment.

Drug price increases have become a major issue on the presidential campaign trail, gaining traction after Turing's price increases were put in the spotlight. Former secretary of state Hillary Clinton has promised to cap drug costs. Vermont Sen. Bernie Sanders (D-Vt.) is opposing President Obama’s nominee to lead the Food and Drug Administration because of pharmaceutical prices. Republican Donald Trump called Turing CEO Martin Shkreli a "spoiled brat." Sen. Marco Rubio (R-Fla.) called price hikes "pure profiteering." A Kaiser Family Foundation poll last week found that high drug prices are far and away Americans' top health concern.

Cummings has been working on this issue since 2011, when the head coach of the University of Maryland women's basketball team wrote to him about a shortage of the drug her son needed to treat his cancer. The shortage was related to profit concerns.

Democrats acknowledged Wednesday that without Republican support, they cannot move legislation in Congress. But, they said, they could prod the other party, as well as the White House and pharmaceutical companies, themselves.

"Shaming is important as well," Rep. Jan Schakowsky (D-Ill.) said.

The Senate, meanwhile, has launched an investigation into Turing, Valeant and a third company.