The government published yesterday new employment figures that key White House officials said show conclusively that the economy is overheating-paving the way for possible new measures to dampen the excess demand that is fueling inflation.

The development came in a new Labor Department report showing that the nation's unemployment rate held steady in March at 5.7 per cent of the work force, bu that the industrial sector continued to boom, dashing hopes that the economy might be cooling.

The figures were expected to prove something of a turning point for the administration. Until now, policymakers had been split about whether the economy was overheating, with some top officials still hestitant about ordering new policy steps.

But key officials said yesterday that the new round of statistics "eliminated any remaining doubts" that the economy is growing too rapidly and bolstered the case that some new action is needed. The only question now appears to be what to do specifically.

One move considered a possibility is for the White House to ask the independent Federal Reserve Board to raise interest rates to dampen demand. Another is to impose selective credit controls to restrict loans to consumers for auto purchases and other items.

The figures yesterday showed these developments:

Despite large increases in hiring in previous months, industry payrolls swelled another 324,000 jobs last month, indicating that consumer demand probably will remain strong in coming months and block any slow-down in production activity.

The department's closely watched index of aggregate weekly hours, a key indicator of the pace of economic activity in industry, rose a sharp 0.8 percent over the month to a level 4.4 percent above that of a year ago.

Employment in the construction industry rebounded visibly last month after falling off in the two previous months, raising new doubts about whether the hoped-for cooling in the housing industry was genuine or merely a fluke.

Carter administration policymakers say the figures confirm the view that it is the economy's overheating, and not some other outside force, that is fueling the latest surge of inflation. Wholesale prices have been soaring in recent months. In March, they rose a full 1 percent.

The figures came as the Council on Wage and Price Stability announced that it has cited 10 more firms for breaching President Carter's price guidelines. Earlier charges against four companies were dropped for lack of evidence.

Meanwhile, the White House, still groping for ways to shore up its flagging wage-price guidelines program, announced that it will aks, informally, a handful of consumer groups to help monitor price increases.

The administration also unveiled a new monthly "national consumer buying alert" pamphlet, intended to advise buyers on price trends in food, housing, energy and medical care. The first, containing basic buying tips, took up 11 pages.

The March report on the jobless rate marked the eighth month that the figure has hovered in the 5.7 to 5.9 percent range. The jobless rate has been on a plateau since last summer, when it fell from 6.2 percent a year ago.

By the measure used by most economists, the nation now is at or near the so-called " full employment" level-the lowest that joblessness can be reduced through general economic stimulus measures without fueling new inflation.

Administration policymakers have been debating whether to try to cool down the overheating by asking the independent Federal Reserve Board to raise interest rates another notch.

The sharp speed-up in inflation over the past few months, due in part to overheating and resulting excess demand, has strained the new wage-price program, which was not designed to deal with that situation.

The administration's new anti-inflation announcements yesterday were regarded primarily as a public relations gesture. Most analysts say they believe inflation will not abat significantly until the economy's growth rate slows.

The figures on payroll employment were regarded as the most significant measure of job growth last month. A second measure, using a survey of households, showed that total employment grew by 195,000 jobs.

The March report on joblessness tends to bolster earlier impressions that the industrial sector of the economy is continuing to boom. Much of the job gain was in manufacturing. And construction employment rebounded.

The new round of statistics left virtually no change in the unemployment rates for major categories of workers. The critical jobless rate for heads of household was 3.4 percent in March, compared with 3.5 percent in February.

At the same time, the politically sensitive jobless rate among black teen-agers fell to 31.5 percent from 35.5 percent in February, as the number of black youths out of work dropped to 334,000.

The overall teen-age jobless rate was 15.5 percent.

The move by the White House to enlist consumer groups in the government's price-monitoring effort involves assigning staffers in the Council on Wage and Price Stability to take reports from the public and investigate them.

Officials said yesterday that the agency would seek aid from purchasing agents, small businessmen, union leaders and consumer groups. The council staff now totals 130, and is scheduled to grow to 233.

The action came after heavy lobbying by an organization called Consumers Opposed to Inflation to the Necessities, a liberal-oriented group that has been pressuring the White House to take a more activist stance.

The group wants Carter to move more aggressively to slow inflation in farm, energy, housing and medical prices. The administration has been arguing that it is doing all that its own, or outside, economists believe can be done. CAPTION: Graph, no caption, The Washington Post