WASHINGTON — Democrats reached a deal on Tuesday to add a measure to control prescription drug costs to President Biden’s social safety net plan, agreeing to allow the government to negotiate prices for medications covered by Medicare, as the House moved closer to a vote on the sprawling bill.

The prescription drug deal is limited. Starting in 2023, negotiations could begin on what Senator Ron Wyden of Oregon called the most expensive drugs — treatments for cancer and rheumatoid arthritis, as well as anticoagulants. Most drugs would still be granted patent exclusivity for five years before negotiations could start, and more advanced drugs, called biologics, would be protected for 12 years.

But for the first time, Medicare would be able to step in after those periods, even if drug companies secure patent extensions or otherwise game the patent system.

“Fixing prescription drug pricing has consistently been a top issue for Americans year after year, including the vast majority of both Democrats and Republicans who want to see a change because they simply cannot afford their medications,” Senator Chuck Schumer, Democrat of New York and the majority leader, said. “Today, we’ve taken a massive step forward in helping alleviate that problem.”

The completion of the prescription drug section could be among the final major changes to a $1.85 trillion climate change and social safety net bill that Democratic leaders hope to bring to a House vote this week. Smaller issues remain to be ironed out, including a way to deal with methane, a powerful greenhouse gas, and the state and local tax deduction, which some House members say must be fully restored to win their votes.

But House Democrats appeared determined to press forward, even without an ironclad commitment by holdout moderates in the Senate to vote for the final package.

The prescription drug compromise was hard-fought and required Democrats to overcome an onslaught of lobbying by the powerful pharmaceutical industry, which succeeded in substantially watering down their initial bid to allow the government to negotiate prices on a far broader universe of drugs. The final deal includes a $2,000 annual cap on out-of-pocket expenditures by older Americans facing catastrophic health issues, a strict $35 monthly cap on insulin expenses and automatic rebates on drugs whose prices rise faster than inflation.

But the pharmaceutical industry won its share of concessions. The inflation rebates initially contained a “look back” provision that would have assessed rebates on drug prices that began to soar as far back as 2012. That would have yielded one-time levies on drug companies in the billions of dollars. And some Democrats wanted Medicare to have price-negotiating authority immediately, with no patent exclusivity periods.

Still, boosters of the compromise believe the negotiating powers it grants Medicare will be a first step toward the broader powers that Democrats have been campaigning on for decades. And, they said, the rules curtailing ever-extending patent protections will be key to lowering costs.

“The problem of evergreening patents so that tiny changes permit these companies to maintain monopolies for years and years and years is wrong,” said Senator Elizabeth Warren, Democrat of Massachusetts. “It violates the basic principle of granting these exclusivity licenses through patents, and has been abused by many of the big drug companies and needs to come to a halt.”

Mr. Schumer was careful to say he had gotten sign-off on the deal from Senator Kyrsten Sinema, Democrat of Arizona and an opponent of the House’s much broader prescription drug proposal.

“It’s not everything we all want. Many of us would have wanted to go much further, but it’s a big step in helping the American people deal with the price of drugs,” Mr. Schumer said.

Ms. Sinema’s office then released a statement declaring, “The senator welcomes a new agreement on a historic, transformative Medicare drug negotiation plan that will reduce out-of-pocket costs for seniors — ensuring drug prices cannot rise faster than inflation — save taxpayer dollars, and protect innovation to ensure Arizonans and Americans continue to have access to lifesaving medications, and new cures and therapeutics.”

Speaker Nancy Pelosi of California privately told her caucus on Tuesday that she hoped to have a vote on the sprawling plan before Congress is scheduled to leave for a Veterans Day recess at the end of the week.

“I’m not announcing a vote, but I did say that this could be resolved by the end of the day,” she said as she left the private meeting.