The nation's unemployment rate unexpectedly dropped from 6 percent in August to 5.8 percent last month, the Labor Department reported yesterday.

Most analysts had expected at least a small increase in unemployment as a result of the current slowdown in economic activity. But the report showed 610,000 more people employed in September than in August.

The September figure put the jobless rate essentially where it has been for most of 1979.

Almost all of the reduction in unemployment between August and September took place among adult women, reversing jobless increases reported as occurring between July and August. This rapid down-and- up suggested to some analysts that the August increase in unemployment was overstated, and that much of the September improvement was also a statistical mirage.

Janet Norwood, commissioner of labor statistics, told Congress' Joint Economic Committee (JEC) that neither the survey of American households nor that of businesses "yet shows any unmistakable signs of labor market recession."

Nevertheless, most economic forecasters still believe the economy, if not already in a recession, will be soon.

But the September employment figures confirm that, after a second quarter decline, the economy recovered somewhat in the third quarter and ended on a strong note.

Economists Walter Heller and George Perry, in a forecast done for the National City Bank of Minneapolis, said, "The forces that have been dragging the economy into recession are somewhat obscured by the economy's mild rebound in the summer quarter."

As the gasoline shortages eased, they said, "a summer uptick (rise) was to be expected before the economy resumed its downward course."

Whatever the reasons, the number of persons unemployed in September fell to 5,985,000 from 6,149,000 in August.

The unemployment rate for adult men remained unchanged at 4.2 percent, while that for adult women dropped from 5.9 percent to 5.5 percent. The rate for teenagers fell slightly from 16.5 percent to 16.4 percent.

Unemployment among black workers also fell, from 11 percent to 10.6 percent. The rate for black teenagers rose from 30.7 percent to 31.5 percent.

The average time a worker has been unemployed rose from 10.5 weeks to 10.6 weeks because most of the drop in unemployment in September came among persons who had been without work for a very short period.

Of those unemployed last month, 2,743,000 had been out of work for less than five weeks. On the other hand, 1,133,000 had been unemployed for 15 weeks or more, and 507,000 of them for 27 weeks or more.

The Labor Department also said that during the third quarter of the year there were 739,000 persons who were not seeking jobs -- and therefore not counted as unemployed -- but would like to have one. These so-called discouraged workers were not actively looking for work for a variety of reasons, including thinking no jobs are available to them. In the second quarter there were 826,000 discouraged workers.

According to the survey of businesses, payroll employment rose by 135,000 last month compared to only a 5,000 increase in August.

Meanwhile, the length of the average work week at such businesses remained unchanged at 35.6 hours. In manufacturing, the average work week dipped from 40.1 hours to an even 40 hours.

Norwood, in her testimony to the JEC, noted, "All of the growth in payroll employment since March has occurred in the service-producing industries. In the goods-producing industries, employment has been on a virtual plateau since March, as small gains in mining and construction were about offset by cutbacks in factory jobs."

Norwood also said that the labor force participation rate -- the proportion of the population either employed or looking for work -- rose to 63.9 percent in September, matching its all-time highs reached last February and March. At that level it is a full percentage point higher than it was in early 1978.

Sen. William Proxmire (D-Wisc.), a member of the JEC, said the September numbers indicate that Congress should not rush into a tax cut to combat a recession that is only a forecast, not a reality.

"We should not pull out the stops and promote tax cuts, public works or business bail-outs on the basis of projected rising unemployment at a time when unemployment is stable or falling," he declared.