The nation's unemployment rate edged down another notch last month while the number of jobs continued to grow rapidly, the government reported yesterday, bolstering fears by some analysts that the economy may be overheating.

The Labor Department's monthly report showed the jobless rate in February at 5.7 percent of the work force, down from 5.8 percent the previous month and the lowest since just before the 1974-75 recession.

Moreover, the number of jobs in the economy increased substantially, reflecting a rapid overall growth rate. Total employment grew by 347,000, following a hefty 445,000 increase in January. Industry payrolls grew by 301,000.

The combination of figures marked bittersweet news for the Carter administration. Although the White House is pleased politically to see the jobless rate drop, officials fear the brisk economy may exacerbate inflation.

Many economists, both in the administration and elsewhere, are worried that the economy has overheated to the point where there now is excess demand -- a factor they say significantly heightens inflationary pressures.

On Thursday, the Labor Department reported that wholesale prices, a harbinger of future inflation, rose by 1 percent in February, the second straight large increase. The price surge was spread throughout the economy.

Some analysts have warned that if this continues unabated, it could lead to a serious recession. A similar situation occurred in 1974.

Meanwhile, in a separate development, the Federal Reserve Board reported that consumers took on less in new debt in February than they have in previous months, in part because of the bad weather. (Article, Page D1.)

The reduction in unemployment levels came primarily among adult workers, particularly in professional and clerical jobs. Yesterday's report showed a record 59.4 percent of the nation's total population was employed.

Jobless rates for most major categories of workers remained basically unchanged over the month, but unemployment among teenagers rose to 16.1 percent, from 15.7 percent in January.

The jobless rate for black teen-agers was 35.5 percent. Analysts say joblessness often hits black teen-agers more severely because so many of those who can't find jobs have no working relatives.

Most of the rise in industry payrolls last month came in the retail trade and other service industries, and in companies that manufacture durable goods, where new orders have increased substantially in recent weeks.

The only major cutback was a modest decline in construction jobs, whose growth is beginning to slow as mortgage rates rise. However, overall employment in construction still is relatively strong.

Despite the slight reduction in February, the unemployment rate has changed little since early last year.

But the total number of jobs has been increasing rapidly since mid-1977. Over the past 12 months, employment has grown by 3.6 million. Industry payrolls have swelled by 3.5 million.

Many analysts believe the economy is at or close to the effective level of "full employment" -- that is, the jobless rate has dropped about as far as it can get without intensifying inflation.

One reason February's sharp growth in new jobs did not push the jobless rate lower is that a sizable number of persons entered the job market during the month. The civilian labor force grew by 301,000 persons.

There were no further signs in February's report of any tapering off in the economy's growth rate. The department's index of aggregate weekly hours in industry rose 0.5 percent, after declining slightly in January.

Janet L. Norwood, acting commissioner of labor statistics, told a hearing of the congressional Joint Economic Committee yesterday that jobless rates "have shown no persistent trend during the past six to eight months."

However, Norwood noted that while the overall level of joblessness has not fallen much in the past several months, the effect of that has not been severe because "the same people have not remained jobless over this period."

Norwood said only half the persons who were unemployed in February also had been out of work in January. The remainders either just began looking for jobs in February or else lost their jobs and were seeking new ones.

The actual number of Americans out of work fell to 5.8 million in February, just a shade under January's level. By contrast, at this time in 1977 there were approximately 6.5 million persons out of jobs.

Norwood also said yesterday the February price indexes showed "a continuing high rate of inflation" and were "not encouraging." She said evidence so far points to "continued upward price pressures for several months.