WASHINGTON — Older Americans have been flocking to Medicare’s private plans, which promise predictable costs and extra benefits.

But the private Medicare Advantage plans have also been getting an unpublicized boost from the Trump administration, which has in the last few weeks extolled the virtues of the private plans in e-mails sent to millions of beneficiaries.

Medicare’s annual open enrollment period closes Friday. Administration officials predict that almost 37 percent of the 60 million Medicare beneficiaries will be in Medicare Advantage plans next year, up from 28 percent five years ago.

The officials deny that they are steering patients to private plans, but the subject lines of recent e-mails read almost like advertisements. “Get more benefits for your money,’’ says a message dated Oct. 25. “See if you can save money with Medicare Advantage,’’ said another sent a week later.

The messages — “paid for by the U.S. Department of Health and Human Services’’ — urge beneficiaries to “check out Medicare Advantage’’ and point to an online comparison tool, the Medicare plan finder.

“You may be able to lower your out-of-pocket costs while getting extra benefits, like vision, hearing, dental and prescription coverage,’’ said an e-mail sent to beneficiaries on Wednesday.

“With Medicare Advantage,’’ says another e-mail, “one plan covers all of your care.’’

In small print, the e-mails say they were “created and distributed by the Centers for Medicare and Medicaid Services’’ to people who “signed up for email updates from the Medicare team.’’

Seema Verma, the administrator of the Centers for Medicare and Medicaid Services, said the agency was not favoring private plans over the original government-run Medicare program.

“We are not steering any Medicare beneficiary anywhere,’’ she said.

But Richard S. Foster, who was for many years the nonpartisan chief actuary of the Medicare program, said the e-mails sounded “more like Medicare Advantage plan advertising than objective information from a public agency.’’

“The statements made in the e-mails are generally accurate, but they are one-sided,’’ Foster said. “The advantages of MA plans are emphasized, while the disadvantages are not mentioned.’’

For example, he said, private plans generally require beneficiaries to use a defined network of health care providers or pay more for care outside the network. By contrast, in traditional Medicare, beneficiaries can go to any doctor who accepts Medicare, as most doctors do.

Jo Murphy, who has counseled thousands of Medicare beneficiaries as the director of Michigan’s Health Insurance Assistance Program, said: “It seems that there are a whole lot of promotional e-mails coming from the federal government. There does seem to be encouragement to go to Medicare Advantage, part of a trend favoring private companies over traditional Medicare, for whatever reason.’’

Federal spending on Medicare Advantage will nearly triple in the coming decade, to $584 billion in 2028, from $210 billion this year, the Congressional Budget Office estimates.

Insurance executives and investors are also bullish on the outlook for the private Medicare plans, offered by companies like UnitedHealth and Humana, which do extensive marketing of their own at this time of year.

When Congress passed the Affordable Care Act in 2010, it helped offset the cost by cutting payments to Medicare Advantage plans. The CBO and other experts predicted that enrollment in the plans would decline. Instead, it has surged to more than 20 million today, from 11 million in 2010.

Democratic members of Congress from Connecticut recently sent a letter to the administration expressing concern that officials were “inappropriately working to steer Medicare beneficiaries to Medicare Advantage plans.’’ The agency has an obligation to “provide beneficiaries with accurate information from a neutral, balanced perspective,’’ said the letter, signed by Senators Richard Blumenthal and Christopher S. Murphy and others.

Even without encouragement from the government, Medicare beneficiaries might be gravitating to private plans.

Many people have become accustomed to managed care plans through their employment. When they reach age 65, they are comfortable opting for a private plan — in some cases, a Medicare Advantage plan offered by the same company that provided their employer-based coverage.

Writing this past week in The New England Journal of Medicine, Patricia H. Neuman and Gretchen A. Jacobson of the Kaiser Family Foundation pointed to other possible attractions.

Medicare Advantage plans offer a variety of extra benefits like dental care and gym memberships, they said. Private plans protect against catastrophic health care costs, with an annual limit on out-of-pocket spending for doctors’ services and hospital care. In addition, they said, private plans “offer the convenience of one-stop shopping for all their coverage.’’

By contrast, beneficiaries in traditional Medicare typically pay one premium for coverage of doctors’ services, another premium for drug coverage and often a third premium for supplemental insurance like a Medigap policy or a retiree health plan.

Ann E. Mason, 77, of Rochester, N.Y., said she was “very, very satisfied’’ with her Medicare Advantage plan. The plan, offered by the local Blue Cross and Blue Shield company, has a network of providers, but most local doctors are in it, she said.

Private plans boast of providing superior-quality care, but the evidence is mixed. Researchers have found that patients in poor health are somewhat more likely than others to disenroll from Medicare Advantage and switch to traditional Medicare.

John J. McAuliffe, 77, and his wife, Ann, 78, were in a Medicare Advantage plan and were generally satisfied with it until she had a severe stroke in Charlotte, N.C., in 2017. After a few months, the insurer refused to pay for further care, and the couple challenged the denial through several levels of appeal until they finally prevailed in a hearing before an administrative law judge.

“We went back to traditional Medicare, with a Medigap supplement policy, and it’s been excellent,’’ John McAuliffe said. “Everything is paid for.’’