One idea addresses an issue that many consider fundamentally unjust: Consumers are increasingly being asked to pay a greater portion of their drug costs, but they don’t get discounts that drug manufacturers offer to health insurers.

The proposal, first floated by federal officials last November, would give at least a portion of that discount to people in Medicare drug plans at the pharmacy counter. The move could lower out-of-pocket costs for people with high drug bills, but would increase the cost of these Medicare plans, offered by private insurers, for everyone. The idea seems to have the support of the Trump administration, including the new health secretary, Alex M. Azar II, a former Eli Lilly executive.

The proposal, which does not need congressional approval, represents the latest clash between powerful health care industries that are engaged in a war for the moral high ground over rising drug prices. The pharmaceutical industry, backed by influential members of the Trump administration, has been lobbying hard for the change, betting that it would act as an escape valve for patients’ anger over drug costs while preserving drug makers’ freedom to set any price they want.

By contrast, the insurance companies and pharmacy benefit managers, which oversee drug plans, are loathe to part with what amounts to billions of dollars in rebate windfalls, arguing that it will lead to higher prices.

The change could present a tidy solution for Mr. Trump, who has come under fire for doing little to follow through on his pledge to lower drug prices, even as he has installed several former drug industry executives in prominent government roles. But it would cost the government money — up to $82.1 billion over the next decade, according to its own estimates.