Medicare’s financial stability has been strengthened by the Affordable Care Act and other forces that have been subduing health-care spending, according to a new official forecast that says the fund covering the program’s hospital costs will remain solvent until 2030 — four years later than expected a year ago.

The annual report, issued Monday by trustees overseeing the government’s two largest entitlement programs, found little change overall in the finances of Social Security. The trustees warned, however, that the part of Social Security that pays monthly benefits to people with disabilities is especially fragile and, without changes, will start to run short of money for benefit checks in 2016.

Taken together, the findings provide a nuanced portrait of the fiscal future of these two programs, which act as cornerstones of social insurance — and a buffer against poverty — for older people and other vulnerable Americans. The trustees welcomed the improved financial prospects for Medicare but acknowledged that the underlying reasons are not yet entirely understood. At the same time, they exhorted Congress to take steps to prevent both programs from collapsing in the long term.

“Neither Medicare nor Social Security can sustain projected long-run program costs,” the trustees said in a message accompanying their reports.

For the past few decades, Democrats and Republicans have fretted about the unsustainability of the Medicare and Social Security programs. They have appointed high-level commissions, proposed legislation and tried to stoke public fears that benefits might not be available for their parents — or themselves. But Congress has not restructured either program to withstand long-term fiscal pressures, and the issue has been absent lately from the agendas of both parties.

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At a news briefing Monday, Cabinet secretaries and two public trustees reiterated the call for Congress to act. “[We] must make manageable changes now, so we do not have to make drastic changes later,” Treasury Secretary Jack Lew said.

“It is getting very late in the game” to find a bipartisan consensus, said the trustees’ only Republican, Charles P. Blahous III, who worked on Social Security and other economic issues as an aide to President George W. Bush. “A solution much further delayed is a solution much less likely to occur.”

Both programs are being strained by the nation’s demographics. As more baby boomers reach retirement age, people 65 and older are making up an increasing percentage of the country’s population, with proportionally fewer working-age Americans chipping in payroll taxes.

Medicare’s finances are facing other pressures, too, including from scientific advances that lead to new treatment and therapies, the report said.

The trustees’ forecast said that the trust fund that pays for hospital care — Medicare Part A — has been strengthened significantly, with the date when it is predicted to start running short of money extended by 14 years since the Affordable Care Act was enacted in 2010. The report also predicted that the insurance premiums that older Americans pay for the portion of Medicare that covers doctors’ visits and other outpatient care would probably remain the same for a third year in a row.

Health and Human Services Secretary Sylvia Mathews Burwell said that it is impossible so far to gauge how much of that trust fund’s improved fiscal health was due to the health-care law as opposed to other changes in the health-care system that are slowing cost increases. She said both had a role. The ACA, for instance, is slowing payments to Medicare Advantage, the part of the program in which older Americans join private health plans, while other provisions focus on curbing hospital readmissions.

The report said that spending on hospital stays last year was less than expected, although trustees noted that analysts have not determined whether this trend reflected broad economic trends or stemmed from specific changes in the practice of medical care.

If Medicare is unchanged by 2030, the year it is projected to become insolvent, it would then be able to pay 85 percent of its beneficiaries’ hospital bills, a proportion that would slip to 75 percent by 2047, the forecast said.

For Social Security, the trustees predicted that the program’s two separate trust funds will, combined, have enough money to pay all the retirement and disability benefits it owes until 2033, the same time horizon as in the last two annual forecasts. They forecast that Social Security will be able to afford checks for retirees and workers’ survivors until 2034 — nearly two decades longer than the part of the program that pays disability benefits.

Social Security’s expenditures last year exceeded its income from payroll taxes, as it has each year since 2010, the report says, although interest so far is making up the difference.

This year, President Obama backed away from an idea he broached in his budget last year to save money for Social Security by changing the basis on which inflation is calculated for the program. But his 2015 budget proposal reprises the idea of charging more for care under Medicare to older Americans who are relatively well-off — an idea that Congress has not touched this year.

In calculating Medicare’s future finances, the trustees for the first time acknowledged that Congress has each year overridden scheduled reductions in Medicare doctors’ fees — cuts that, if adopted, would lower payments for doctors’ services by 21 percent in 2015. In the latest report, the trustees assumed that such cuts would continue to be waived.

The trustees noted that their new forecast was released 49 years to the week that President Lyndon B. Johnson signed the law that enacted Medicare, a major component of the Great Society programs of the mid-1960s. Social Security was a response to the Great Depression of the 1930s.

Last year, Medicare insured 52 million Americans, including 43.5 million age 65 and older and nearly 9 million younger people with disabilities. Social Security last year provided benefits to 41 million retired workers and their families, 6 million survivors of workers who died, and 11 million working-age people with disabilities.