WASHINGTON — The government said this morning that Medicare’s hospital trust will not be exhausted until 2026, two years later than projected last year, while the date that Social Security will exhaust its trust fund remained unchanged at 2033.

The latest projections were included in the annual report of trustees of the trust funds. The new report warned that despite the small improvement in Medicare, both it and Social Security face significant funding challenges as the giant baby boom generation continues to retire.

Currently, 58 million Americans are receiving Social Security benefits.

The reasons given for the improved financial outlook for Medicare were an overall slowdown in health care spending, particularly on skilled nursing care, as well as lower projected costs for popular insurance plans available within the Medicare program.

Treasury Secretary Jacob Lew, the chairman of the trustees, said President Barack Obama is committed to working with Congress to put both programs on a stronger footing.