A Harvard University team of doctors and health economists yesterday recommended a major expansion of Medicare to cover long-term nursing home care for the aged and to provide insurance against the costs of "catastrophic" illness.

The plan would also reduce costs now paid by Medicare patients, improve home health care benefits and require doctors who treat Medicare patients to accept the Medicare-allowed fee as full payment.

The catastrophic-illness feature would limit out-of-pocket payments for elderly persons to $1,000 a year for covered services, including all doctor and hospital costs.

The proposal, based on a two-year study, was drafted by a group of 14 doctors and health experts, including former surgeon general Julius B. Richmond, physician David Blumenthal and others from the John F. Kennedy School of Government and related Harvard units. Laid out in a New England Journal of Medicine article and in a news conference here, the proposal comes just as President Reagan has ordered a major study on catastrophic-illness insurance.

The central feature of the plan is to relieve the relatively few Medicare patients who need prolonged hospital care or long-term nursing home care from paying the often overwhelming costs themselves. At present, Medicare does not pay full costs after a patient's 60th day in a hospital; few people stay that long, but those who do often face bankruptcy. Nor does Medicare pay for long-term nursing home costs, although 1.5 million people are in such homes and the number is expected to double over the next generation or so.

The added cost to Medicare of the nursing home benefits, catastrophic-illness protection and reduction of other out-of-pocket payments recommended in the plan was estimated at as much as $49 billion annually by the year 2000. The plan would relieve the aged of about $35 billion in out-of-pocket and insurance fees.

About $25 billion of new Medicare costs would be offset by increasing Social Security taxes, part of which are used to fund Medicare, by an additional 1 percent of salary each on employers and employes (for an eventual total Social Security tax of 8.65 percent on each).

Another $11 billion or so would be obtained by shifting to Medicare the federal general revenue funds now used to pay for nursing home care in the Medicaid (low-income medical) program.

Remaining needed funds would come from several sources, including a 5 percent "surtax" on income taxes paid by the aged, elimination of the extra $1,040 federal income-tax exemption for taxpayers 65 and over, and an increase in the Medicare premium (now $186 a year) of about $150 to $200 a year for all but low-income Medicare enrollees.

The proposal differs sharply in its approach from current Reagan administration policies, especially in its heavy reliance on direct government taxing and fund-allocating mechanisms. It maintains the current structure of Medicare as a centrally run federal health insurance system for the aged, which has long been a favored Democratic approach to health coverage, and could serve as the framework for Medicare changes if Democrats gain control of the White House or Senate.

The administration, on the other hand, dislikes the idea of enlarging the central government role and instead favors a system of vouchers -- worth the insurance cost of Medicare -- that would allow recipients to buy their own policies from private insurers and prepaid group plans. The administration has argued that the marketplace would assure cost-effective delivery of medical services.

In directing the Department of Health and Human Services to study how to insure against catastrophic medical costs, the president has made clear that he wants solutions to lean heavily on the private insurance industry.