Administration health officials will urge President Carter today to support an expansion of roughly $20 billion in the nation's health insurance to counter Sen. Edward M. Kennedy's proposal for even broader coverage.

Health, Education and Welfare Secretary Joseph A. Califano Jr. will give the president a range of options to fulfill his election campaign promises to improve Americans' protection against the high cost of medical care.

The options, administration sources said yesterday, will average out to "something close to" $20 billion a year-perhaps $15 billion of it in federal funds and the rest in private money-to finance an expansion in Medicare and Medicaid plus new coverage for serious or catastrophic illnesses.

The programs, if Carter accepts them, would make up the "first phase" of the administration's national health insurance program. So far the president and Califano have said only that the president would urge a $10 billion to $15 billion" program.

Officials in the Office of Management and Budget and in the Council of Economic Advisers still would like to keep initial costs as low as possible and could prevail, sources said.

On Monday, Kennedy and 65 national groups-the AFL-CIO, the National Association for the Advancement of Colored People and others-backed a broad health insurance program that would start in 1983. It would eventually add $40 billion in current dollars to the nations's health insurance bill-$28.6 billion in federal funds, $11.4 billion in private money.

At the same time, the chairman of the Senate Finance Committee, Russell Long (D.La.), is pushing a plan that would simply add a possible $5 billion to $10 billion in catastrophic illness coverage to the nation's health insurance.

Califano has said repeatedly that adding catastrophic coverage alone would "skew" the country's health care system even further toward expensive, last-ditch care for patients often hopelessly ill.

"The issue of how much the president will support is still undecided," an informed source said. But the political pressure will be, first, to offer more than Long's catastrophic plan alone, if the president wants labor and minority support-and, second, to offer Congress something it is more likely to support than Kennedy's $40 billion expansion.

The plan most favoured by HEW officials, according to one person, includes:

An increase of apprxomately $12 billion in federal Medicaid expenditures for the needy-to standardize and improve the present, hugely varying Medicaid programs in 49 states and provide Medicaid in Arizona, the one state that has never provided it.

An increase of roughly $2 billion in federal Medicare for the aged and disabled-to-eliminate or reduce the payments Medicare patients now must make after their first 60 days of hospitalization.

Another $1.5 billion in federal funds to add approximately one million persons to Medicare coverage-recent immigrants, fomer federal and state workers and the seldom-employed who have never become eligible.

A new law ordering private employers and employes to add at least $5 billion to their coverage for serious and catastriohic illnesses.

A "basic mandated plan" would limit workers' families' annual outlays for health care to a possible $2,500 a year. A reinsurance pool-of undetermined size-would pay for truly catastrophic illness, possibly those costing more than $25,000 or $30,000 in any year, so no single insurance firm or employer would have to bear these high risks.

The federal government, finally would add $200,000 to $300,000 in federal funds to help firms that cannot afford high enough health insurance premiums for their employes.