President Carter sent Congress yesterday a "lean and tight" $500.2 billion budget for fiscal 1979 that would increase spending barely more than is needed to offset inflation and would shrink the impact of government on the economy.

The spending plan contains virtually no major new initiatives. Carter asked for a small increase in job-creation programs and promised to propose a new urban-aid plan sometime this spring. He recommended a sizable increase in defense spending.

Despite the absence of major new progarms, the budget would produce a deficit of $60.6 billion, essentially unchanged from this year's $61.8 billion red-ink total. The President pointed out tht part of the deficit would stem from the $24.5 billion net tax cut he is proposing.

Nevertheless, the relatively conservative spending plan would take Carter a step toward his goal of reducing the share of the Gross National Product taken by the federal government. Yesterday's budget proposal would trim this federal share to 22 per cent, from 22.6 per cent the year before.

The spending plan is important because it is the first that Carter has decided on his own. The fiscal 1978 budget, which covers the period through next Sept. 30, was largely set by the outgoing Ford administration. When Carter took office there was only time to make minor changes.

But the changes he made this year were hardly major ones. Carter's $500.2 billion spending recommendation represents a net increase of only $7.8 billion, or 1.6 per cent, from the $492.4 billion it would cost just to maintain current federal benefits and service in the face of inflation.

The tax cut is by far the most significant policy initiative in the budget. It would cut taxes for individuals and corporations at the start of the fiscal year, beginning Oct. 1, and would liberalize tax incentives for business investment effective this past Jan. 1.

Significantly, the fiscal 1979 budget contained no provision for the new national health insurance progarm Carter promised during the 1976 campaign. And it included only a modest $200 million in start-up money for his new welfare "reform" plan, another election-year pledge.

The budget estimates that, in line with the administration's new anti-inflation program, next October's federal pay rise will be about 6 per cent. That is also the estimated rate of inflation this year and next.

The Budget proposes raising the prices that middle-income and upper-income children are required to pay for school lunches; expanding birth-control services to teenagers as an alternative to the abortions Carter opposes; and expanding the federal college scholarship programs to make more middle-income students eligible and counter pressure for a college tuition tax credit.

Carter also asked Congress to increase the appropriation for civil rights enforcement, partly in anticipation of increased school desegregation litigation. At the same time, he proposed a small reduction in personnel at the FBI, which he also said would shift emphasis and spend less time in the future chasing bank robbers.

In his Budget Message to Congress, the president called his spending plan "restrained," but asserted that it was "nevertheless directed toward over-coming out nation's crucial problems." He said his major priority was seeing to it that the economic recovery continues intact.

The President projected that his spending and tax proposals together would help keep the economy growing at a moderate 4.75 per cent pace in 1978, with the jobless rate dropping to an average of 6.2 per cent in the final quarter, from 6.4 per cent now.

Reaction to the President's proposal predictably was mixed, with Democrats generally complaining the president had been too tight-fisted, adn Republicans chiding the administration for overspending. Most observers expect that Congress will increase spending beyond what Carter proposed.

Rep. Robern N. Giaimo (D-Conn), chairman of the House Budget Committee, said Carter's plan was "a move in the right direction," but expressed concern that stimulating the economy through a tax cut rather than new spending programs might not take care of the nation's hard-core unemployed.

Sen. John Tower (R-Tex) and Sen. Dewey Bartlett (R-Okla.) critized the defense budget as too low. Tower called Carter's recommendation "far too modest a level to adequately respond to the seriousness of the Soviet military challenge." Bartlett called it "dangerous inadequate."

Yesterday's budget proposed overall spending increases of $38 billion, or 8.2 per cent above the $462.2 billion total estimated for the current fiscal year. After adjustment for inflation, this represents a rise of 2 percent - the smallest in four years.

However, Carter asked for a substantial increase in "budget authority" - permission to start projects that would obligate funds for future years. Total budget authority would rise to $568.2 billion - a jump of $65.3 billion, or 13 percent, from the current year.

The new Carter budget contains these elements:

Defense spending. A rise of $10.2 billion, or 9.4 percent, to a new total of $117.8 billion - largely to bolster the North Atlantic Treaty Organization, develop the cruise missile and test the B-1 bomber.

Energy. An increase of $1.8 billion or 22.9 per cent, from last year's level of $7.8 billion - mostly to cover the cost of the President's energy-conservation program and increase spending for fossil-fuel research - a major shift away from earlier emphasis on nuclear reactors.

Foreign aid. A sharp 23 per cent increase in budget authority for foreign assistance, mostly to support aid to needy nations by the International Monetary Fund and World Bank. Except in the case of arms for Middle East nations, foreign military assistance, which Carter has promised to curb, would decline slightly, in favor of sales credits.

Jobs. A $400 million increase in job-creations monies to begin a new program to reimburse private industry for training unskilled youths and start demonstration projects for the jobs portion of the welfare program. Carter also would continue existing public-service jobs.

Education. A $1.4 billion increase in education spending, to $12 billion, mostly for increased federal aid to the disadvantaged and handicapped and for the new scholarships for middle-class college students to head off pressure for a tuition tax credit.

Cities. Carter pledged a new aid package for urban areas, but left the details - and the price tag - for later this spring. Most observers expect only a modest program, built primarily around loan guarantees to New York and other hard-pressed cities.

Except for defense and a handful of other programs, virtually all the increases were held to the spending levels needed to continue programs intact after accounting for inflation. Defense outlays were 7 percent above this "current services" level.

Despite the hefty increase in defense spending, Carter's proposals would reduce the proportion of military spending compared to outlays to human resources programs. At the same time, it would continue Ford's policy of boosting defense spending faster than inflation.

Carter contended in his budget message that despite the sharp increase, the defense budget still was $8 billion below what Ford last estimated for fiscal 1979, and therefore was "consistent with" his own campaign pledge to slash military spending by $5 billion or more.

The main thrust behind the new Carter budget proposal was to keep the economic recovery intact by enacting a tax cut to offset the "drag" on the economy created by the combination of inflation and new Social Security tax increases.

James T. McIntyre Jr., director of the Office of Management and Budget, said Carter specifically rejected the option of trying to stimulate the economy through increased spending. McIntyre said if more stimulus is needed later, it, too will come through a tax cut.

In proposing his budget yesterday, Carter all but abandoned his campaign pledge to balance the federal budget by 1981 - asserting only that "this budget places us on a path that will permit a balanced budget in the future if the private economy continues its recovery in coming years."

Technically, the White House projected that if the economy performs as expected, the budget will run an $8.6 billion surplus by 1981. However, officials conceded that such long-term predictions are shaky. And the Administration based them on optimistic economic forecasts.

But McIntyre told reporters that "it might be that we will have to defer the balanced budget goal" if it becomes necessary to cut taxes again in coming years. And he conceded it was likely the administration will propose another tax cut before 1981 to offset Social Security taxes.

It was only a year ago that Carter was predicting confidently that because of continuously rising income tax revenues the budget would be in surplus by $60 billion in 1981. The president said then he planned to use this "fiscal dividend" to finance new social programs.

Carter also backed away from his earlier attempts to cut back spending on dams and other water projects, which embroiled him in a battle with Congress during his first months in office. The new budget allows full financing for all such pending programs, though it recommends no new starts on the grounds the administration is now making a general study of federal water policy and will not have results until spring.

In broad distribution terms, the budget had essentially the same look as in previous years. Nearly one-fourth of total spending was earmarked for defense; one-fifth for Social Security and a tenth for interest on government borrowing. These three major items make up just over half the budget.

Add just four more programs - Medicare, Medicoid, unemployment compensation and pension checks to retired federal employees - and two-thirds of the total is reached. The remainder of the government is run on the other third.

Yesterday's budget was the first to prepared under Carter's "zero-base budgeting" procedures, in which individual departments and agencies are required to rank their spending priorities in detail to give policymakers a better grip on the budget.

Although Carter insisted in the Budget Message that "because of this system the budget, includes dollar savings," officials were unable to estimate how much, if any, the new process has saved. McIntyre said OMB would publish a report on the program's results next month.

Despite official unconcern about the size of the budget deficit, the $60.2 billion red-ink figure Carter is projecting was expected to heighten inflationary psychology in the business community. By most economic theory, the deficit should be declining in a recovery.

W. Michael Blumenthal, the secretary of the treasury, estimated that this year's deifcit would require some $70 billion in government borrowing - about $12 billion to $15 billion higher than the fiscal 1978 figure - pushing the national debt to $690.8 billion, from $617.8 billion now.

However, Blumenthal insisted that credit markets would be able to handle the flow because there's more money available now for investment and lending. The secretary scoffed at predictions by some economists that the increase might "crowd out" some private borrowers.

The $70 billion figure includes borrowing requirements for so-called "off-budget" agencies and quasi-public entities, such as the Postal Service and Export-Import Bank, whose spending is not included in the regular budget. Outlays by these agencies would add an estimated $14.8 billion to the budget.

Only about $5.5 billion of the $30 billion in spending changes Carter has proposed would require formal legislative approval. The rest is in projects pegged to caseload or inflation levels, or else continue spending levels of previous years.

For all its parsimony, Carter's budget for fiscal 1979 contained surprisingly little of the budgetary shenanigans policymakers often use to juggle overall spending and deficity figures for political purposes. Examples of this typically are inflated estimates for receipts from offshore oil leases.

As have most presidents before him, Carter proposed cutting the "impact aid" program that provides grants to local school districts in areas with high concentration of federal employees - a cutback Congress repeatedly has refused to approve.