WASHINGTON — In his zeal to fulfill a campaign promise, President Trump has correctly identified high drug prices as a major problem for many Americans. But in defending his proposed solutions, he has sometimes stretched the facts.

Mr. Trump has proposed that Medicare pay for certain prescription drugs based on the prices paid in other developed countries. He called this “a revolutionary change” and said it would save money for the government and for Medicare beneficiaries without hurting their ability to get the medicines they need.

As part of a demonstration project covering half the country, Medicare would establish an “international pricing index” and use it to calculate a “target price” for each drug covered by Part B of Medicare. The proposal is expected to produce “a 30 percent reduction in Medicare spending” for drugs included in the test, the Department of Health and Human Services said.

The new pricing model, unveiled less than two months ago, has encountered a torrent of criticism from drug companies, which benefit from high prices under the current system, and from conservative groups, which accuse Mr. Trump of trying to import price controls from foreign countries.

Part B of Medicare spends roughly $30 billion a year for drugs that patients receive in doctor’s offices and outpatient hospital clinics — often by infusion or injection — for cancer, rheumatoid arthritis, macular degeneration and other conditions. Some of the drugs cost more than $100,000 a year. Many are biologic drugs made from living cells.

What was said

U.S. drug companies voluntarily cut the price” of drugs overseas far below what they charge in the United States “for the exact same drug.”

— The Trump administration, in statements this fall.

Mr. Trump is right that brand-name drugs often cost much more in this country than in Europe. But it is a stretch to say that drug companies voluntarily provide discounts abroad. They generally charge lower prices to ensure that their products will be covered by national health systems in other countries.

Medicare does not use its leverage in that way. As a candidate, Mr. Trump said Medicare should directly negotiate prices with drug makers, a proposal long favored by Democrats. But since taking office, he has dropped the idea.

Most of the 36 countries in the Organization for Economic Cooperation and Development “regulate pharmaceutical prices directly or indirectly through coverage determinations,” the group said in a report last month.

Daniel Hartung, an associate professor at the Oregon State University College of Pharmacy, explained: “Many O.E.C.D. countries have single-payer systems in which the government is essentially setting prices and telling companies what it will pay for coverage. That’s how they can extract substantial reductions relative to prices paid in the United States.”

Mr. Trump is proposing to use prices in 14 other countries as a benchmark or guide in deciding what Medicare would pay. The administration acknowledged that some of these countries, like the Czech Republic and Greece, “have far lower per capita incomes than the United States.”

Several of the 14 countries have a budget for spending on prescription drugs. Many peg their payments to drug prices in other countries, a practice known as reference pricing or international benchmarking. Some of the countries assess the “cost-effectiveness” of drugs and limit how much they will pay for expected gains in the length and quality of life, with some exceptions allowed.

Just seven months ago, the Trump administration criticized the use of reference pricing by other countries, but it has now proposed something similar for Medicare.

What was said

“The president is also going to bring smart negotiation to billions of dollars’ worth of drugs in a part of Medicare where there is currently no negotiation at all.”

— Alex M. Azar II, the secretary of health and human services, in May

What was said

“In Medicare Part B today, the government gets the bill, and we just blindly pay it — oh, plus a 6 percent markup for the provider who administers it. There is no negotiation.”

Mr. Azar in October

It is true that the government does not negotiate with drug manufacturers to determine the prices paid for drugs in Part B of Medicare. But the prices paid for many of those drugs do reflect the results of competition and negotiations in the private sector.

Under the Medicare Modernization Act of 2003, the government’s payment for a Part B drug is based on the drug’s “average sales price.” This price, as defined in the law, accounts for commercial discounts, rebates and other price concessions that drug manufacturers negotiate with health insurance plans, pharmacy benefit managers and other private purchasers.

These price concessions, generally treated as trade secrets, may knock 15 to 35 percent off the list price of a drug.

The problem for Medicare and for consumers is that, for some drugs, manufacturers do not give substantial discounts. This may be the case, for example, if a drug has no direct competitors, so doctors cannot prescribe an alternative, or if the market for a drug outside Medicare is small.

“For at least 30 percent of Part B spending, Medicare prices are at least half of the market, meaning there is effectively no competition within that substantial federal spending among competing products,” said John O’Brien, the senior adviser on drug pricing at the Department of Health and Human Services.

What was said

“This model will expand patient access, through lower prices. This is a pro-patient-access model. We are going to lower drug prices substantially, for our most costly drugs, without restrictions on patient access.”

Mr. Azar in October

Under Mr. Trump’s proposal, Medicare payment for physician-administered drugs would be based, in part, on prices in other countries, including some that restrict access to drugs by limiting coverage.

The administration assumes that Medicare can pay lower prices without limiting access. This assumption is based on a belief that drug manufacturers could not walk away from the Medicare market because it is so large, with 55 million people in Part B.

Moreover, Medicare officials say they would monitor the use of prescription drugs to ensure that beneficiaries’ access to medicines is not compromised. Even with the pricing index, they say, Medicare would still be paying more than the average of other countries.

But some advocates for patients are apprehensive.

“We share the administration’s goal of reducing prescription drug costs,” said Christopher W. Hansen, the president of the advocacy arm of the American Cancer Society, but the proposal “raises numerous questions about beneficiary access.”

“For instance,” Mr. Hansen said, “how would patients access necessary care if there are no vendors willing to bring drugs to physicians in their area? What if the drug maker decides not to sell a particular drug at the price required under the proposal, and patients are unable to get the Medicare-covered drugs they need to treat their disease?”

Dr. Debra Patt, a breast cancer specialist at Texas Oncology, a group of more than 400 doctors, asked: “What leverage would a vendor have to bring manufacturers to the table? Suppose a manufacturer is selling drug X for $1,000, and the vendor wants to pay only $750. What if the manufacturer says no? What then happens to Medicare beneficiaries?”