WASHINGTON—A pair of centrist House Democrats are expected to soon release their own proposal for lowering the cost of prescription-drug prices, as the party tries to close internal divisions over a popular plank of its $3.5 trillion social welfare and climate package.

The legislation from Democratic Reps. Scott Peters of California and Kurt Schrader of Oregon takes a narrower approach to a key provision of the broader House Democratic plan, which would allow Medicare to negotiate over the price of prescription drugs.

The centrist Democrats’ proposal would allow those Medicare negotiations under more limited circumstances than the broader Democratic plan, unveiled Thursday, likely to produce a smaller impact on the industry and reduced savings for the federal government.

The centrists’ bill is also backed by Democratic Reps. Kathleen Rice of New York, Stephanie Murphy of Florida and Lou Correa of California.

Mr. Peters said in a statement that the plan aims to both lower out-of-pocket drug costs for consumers while also protecting drug-industry jobs and investments in future innovation.

Striking a compromise on prescription-drug pricing will be key for Democrats trying to muscle through a sweeping package of healthcare, education and climate provisions through two narrowly divided chambers.

In the House, Democrats can afford no more than three defections on legislation expected to be opposed by all Republicans. In the evenly divided Senate, the Democratic caucus must remain united to pass legislation under a process tied to the budget, which allows it to sidestep GOP opposition.

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In addition to being popular with the public, the goal of lowering the cost of prescription drugs is an important component of the roughly $3.5 trillion package because it is expected to save the federal government hundreds of billions of dollars, offsetting spending on other healthcare programs. Some centrist Democrats in both chambers have said they would like to see the full package entirely offset by revenue and savings, although Democratic leaders have indicated they aren’t sure whether that will be possible.

The legislation from Messrs. Peters and Schrader would allow Medicare to negotiate price concessions of 25% to 35% on drugs that don’t have competition on the market and aren’t protected by exclusivity, which is a period when a drug is protected from generic drug competition, according to a summary of the bill.

That is a more limited scope than the legislation unveiled by the House Energy and Commerce Committee on Thursday, and previously passed by the House in late 2019, which is part of the panel’s portion of the broader budget package.

“We have a historic opportunity to take bold action that delivers meaningful change for the American people, and I look forward to coming together to take up this urgently needed legislation,” House Energy and Commerce Committee Chairman Frank Pallone (D., N.J.) said in a statement about the committee’s portion of the package Thursday night ahead of a vote scheduled for next week.

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The committee legislation, backed by House Speaker Nancy Pelosi (D., Calif.), would allow Medicare to negotiate prices with drug companies over a group of the most expensive and commonly used drugs that don’t face competition, as well as insulin. Under this system, the Health and Human Services secretary could negotiate on the price of 25 eligible drugs the first year, followed by 50 drugs in subsequent years. Those negotiated prices couldn’t go above 120% of the drug’s average price in a group of international countries.

Under the committee’s approach, health plans that participate in Medicare, as well as health plans on the commercial market, would have access to those prices. If companies refused to negotiate or didn’t agree to the price, they would be subject to an excise tax of up to 95% of that drug’s sales.

That system is controversial, including with Mr. Peters and with drug companies, which say it amounts to government price controls that would slash their revenue and their ability to fund the research and development of new treatments.

“The word ‘negotiation’ sounds extremely reasonable, but we are not talking about negotiation,” Kenneth Frazier, executive chairman of Merck & Co., said on a call with reporters this week. “The [HHS] secretary gets to propose prices to the industry and if the industry does not ultimately agree to those prices, there’s a penalty of 95%. It is in fact a substitute for the word price controls.”

Other Democrats have said it is unfair that Americans often pay higher drug prices than residents of other developed countries. Republicans have said Democrats’ approach would reduce innovation at drug companies and limit patients’ access to treatments.

The Energy and Commerce Democrats’ bill would also cap out-of-pocket costs for beneficiaries of Medicare’s prescription-drug benefit program at $2,000 a year. The centrist Democrats’ approach would adjust that cap along with income, providing lower out-of-pocket costs to the poorest Americans on Medicare.

They would establish a $1,200 annual out-of-pocket cap for those people with incomes at 300% or less of the federal poverty level, a $2,000 cap for those with incomes between 300% and 400% of the federal poverty level and a $3,100 annual cap for those above 400% of the federal poverty level. They would also impose a $50 monthly out-of-pocket maximum on insulin.

The Congressional Budget Office estimated that an earlier version of the drug-pricing legislation that passed the House would lower spending by about $456 billion over 10 years. Democrats plan to use much of that on other healthcare programs, including expanding Medicare benefits to include dental, health and vision and providing healthcare coverage for some people in states that didn’t expand Medicaid.

In the Senate, Finance Committee Chairman Ron Wyden (D., Ore.) has released a set of principles for lowering drug prices that include enabling Medicare to negotiate, but his panel hasn’t yet released its own detailed proposal.

Write to Kristina Peterson at kristina.peterson@wsj.com and Stephanie Armour at stephanie.armour@wsj.com