President Carter said yesterday that he will not propose a tax cut in the budget he will send to Congress next week, but left open the possibility of tax reduction later in the year if the economy weakens more than expected.

In a 75-page written State of the Union message to Congress, Carter set forth a modest legislative program, placing highest priority on proposals left over from last year, and said his chief objective this year will be to reduce inflation by holding real growth in federal spending to "close to zero."

He acknowledged in the message that inflation is adding to the tax burden by pushing taxpayers into higher tax brackets, but said that the enactment of tax cuts to offset that trend must await further evidence that the economy is entering a recession and that inflation is cooling.

Asserting that the predictions of a recession may be in error, the president said:

"To enact tax cuts now would run a serious risk of adding inflationary demand pressures to an economy which continues to grow more strongly than predicted by the forecasters.With the present high inflation, we cannot afford that risk."

If a tax reduction does become necessary later in the year, Carter said that "serious consideration" should be given to a reduction in Social Security taxes; half such a cut would go to business and ease upward pressure on prices. Most proposals along these lines do not call for an actual cut, but a deferral of the scheduled Social Security tax increase next Jan. 1.

The president said his highest and most immediate legislative priority remains enactment of his proposed oil tax, which would provide the funds for many of his other energy proposals. House-Senate conferees were meeting on the tax last night, working to narrow their few remaining differences.

Overall, the message contained no surprises and continued the administration's emphasis on fiscal austerity. Among a detailed list of other items and a recitation of earlier of administration accomplishments, Carter:

Said he will propose a $12 billion program in grants and loans to utility companies to encourage conversion from oil to coal as a source of power generation.

Said he will propose new legislation dealing with nuclear waste management and to revamp the Nuclear Regulatory Commission. But the president reaffirmed his support for nuclear energy, saying that once safety reforms are achieved "we must resume the licensing process promptly so that the new [nuclear power] plants which we need to reduce our dependence on foregin oil can be built and operated."

Said the budget for the fiscal year that begins next Oct. 1, and which the will send to Congress next week, will include funds for 300,000 additional federally subsidized rental units -- up from 250,000 this year -- and 25,000 subsidized units for homeowners.

Called for enactment of his national health insurance program and in the process took a swipe at the more ambitious health plan of a Democratic presidential rival, Sen. Edward M. Kennedy (D-Mass.). Carter urged Congress to compare his proposal with "the alternatives -- programs which either do too little to improve the health care needs of Americans most in need, or programs which would impose enormous financial burdens on the American taxpayers."

Said he will propose legislation to allow the various trust funds within the Social Security system to borrow from one another. "This would be aimed at allowing the Old Age and Survivors Insurance Trust Fund, whose reserves shrank last year to borrow from the Disability Insurance Trust Fund, whose assets increased last year.

Promised a "generous increase" in funding for education programs, but provided no specific budget figures. He said his education proposals will include "significant increases in a number of programs serving special populations, in addition to the major new program designed to give youth the basic skills needed to get and keep a job."

Traditionally, the president's lengthy written State of the Union message has been made public the same day as or just after his State of the Union address to a joint session of Congress. White House officals said the written message was released early this year because Carter's speech to Congress Wednesday night will largely deal with foreign policy questions, particularly the crises in Iran and Afghanistan.

Release of the message yesterday also concided with last night's Iowa precinct caucuses, providing the president with exposure on evening news broadcasts just before Iowa Democarts met to begin the 1980 presidential election process.

The message contained no specific budget figures. Officals said the fiscal 1981 federal deficit will be less than half the current year's deficit -- now calculated at $33.2 billion -- suggesting about a $16 billion deficit in the next fiscal year.

Carter came to office vowing to balance the budget by the last year of his term. He failed, but still asserted that if the economy remains strong enough to maintain employment at its current level, the government would end fiscal 1981 with a surplus.

In addition to nuclear waste management legislation and the proposal to encourge utility conversion from oil to coal, the president said he will send Congress only four other new legislative recommendations this year.

These include a $2 billion youth employment program, a five-year, $6.9 billion-a-year extension of the general revenue-sharing program with states and cities, and the details of a standby gasoline rationing program that Congress empowered Carter to devise lat year. The president said he does not now plan to impose rationing.

The other new measure will encompass legislation to implement the U.S. response to the Soviet invasion of Afghanistan, including proposed aid to Pakistan.

A senior White House official, noting that in a presidential election year the Congress will have only about 80 legislative days in which to work, said the scope of the administration program was deliberately held down so that Congress can concentrate on eariler but still pending adminstration proposals.

Among the pending measures on which Carter called for action was the hospital cost containment proposal, which he termed "the single most important piece of legislation that the Congress can pass to demonstrate its commitment to fighting inflation."

Suggested the possibility of expanded trade with China and other nations as a means to offset the suspension of some trade with the Soviet Union.

Warned that he is distrubed by pending water projects legislation on Capitol Hill and what he called a "legislative assault" on the Federal Trade Commission.

Said his highest enviromental priority is enactment of legislation to protect lands in Alaska.

Reiterated his support for the Equal Rights Amendement, the D.C. Voting Rights Amendment and legislation to make Martin Luther King Jr.'s birthday a national holiday.

Much of the message was a review of past administration efforts to overhaul various government processes, and a reafirmation of the president's commitment to government reorganization.

On tax policy, a White House official said that if the economy "significantly deteriorates" the administration will be ready with "a variety of measures" to offset the impact. But he said there is no "automatic trigger" that will bring forth a tax cut proposal and that the administration will rely on a month-by-month monitoring of the economy to make its decision.