Ronald Reagan's health advisers are urging him to press for a national catastrophic health insurance system under which everyone in the country would be insured against illnesses costing more than some fixed amount. But they say this should be mainly done through the private sector, not a large new government-financed program.

They also urge unspecified steps to introduce more competition into the health care system, partly by giving patients more choice than they generally have today between high-cost and low-cost insurance plans. They believe this would encourage patients to shop around for the best insurance deal, and thereby encourage insurance companies themselves to police costs much more than now.

A report by the president-elect's Health Policy Advisory Group, headed by Dr. William B. Walsh, medical director of Project Hope, backed universal catastrophic insurance as one goal of health policy. The report has not been released yet, but several panel members described its contents. Reagan himself, during the campaign, advocated catastrophic coverage instead of comprehensive national health insurance.

Under catastrophic health policies, the individual pays the first few thousand dollars of a year of his medical bills, then the policy pays virtually all the rest. The individual is thus protected against long and costly illness. Advocates of comprehensive national health insurance contend that catastrophic insurance by itself is inadequate because millions can't afford to pay the first few thousand dollars.

Although the report doesn't spell out precisely how to achieve universal coverage, it says that a first step could be to use the tax code to encourage more employers to provide health insurance, including catastrophic coverage.

The report says that insurance companies should be encouraged to set up large pools where people not covered on the job would be guaranteed the right to "buy in" at relatively moderate rates.

The report doesn't spell out precisely how non-working poor people would find the money to "buy in." Some, it indicates, would be covered by the existing Medicaid program for the poor, and others by Medicare for the elderly and disabled.These people, the report says, might be given government vouchers and allowed to buy private insurance, in order to shift basic payment and handling to a private basis. The government would pay for the vouchers and the individual would then go out and purchase the most suitable policy.