Increased layoffs, mostly of women and blacks, pushed the nation's unemployment rate to 6 percent last month, the Labor Department said yesterday. The report was issued as a key White House official made the administration's gloomiest-yet prediction for prices in 1980.

The layoffs boosted unemployment by 200,000 to 6.2 million persons in October, the department said. The unemployment rate, which hit 6 percent in August, had fallen back to 5.8 percent in September.

Robert Russell, director of the Council on Wage and Price Stability, said he expects consumer prices to go up at a 9 percent 10 percent rate during 1980.

Russell also indicated he expects little slowdown in the current 13-percent rate before the end of year. Consumer prices have climbed just about that fast all year, and Russell said prices would be up between 12 percent and 13 percent for the year as a whole.

Even though there has been no abrupt surge in unemployment, it is increasing steadily. During the second quarter of the year, the number of people out of work averaged 5,880,000. In the third quarter it rose to 5,994,000, and last month reached 6,182,000.

Of that total, 2,771,000 lost their last job while only 825,000 voluntarily left it. The remainder of the unemployed either are seeking their first job or have reentered the labor force after being out of it for some time.

The increased layoffs were largely responsible for a rise in the unemployment rate for adult women from 5.5 percent in September to 5.8 percent last month. Similarly, the rate for black workers rose from 10.6 percent to 11.7 percent.

The unemployment rate for adult men ticked up from 4.2 percent to 4.3 percent. The rate for white workers rose from 5.1 percent to 5.2 percent, and for teen-agers, from 16.4 percent to 16.6 percent.

Most economists, including those in the Carter administration, expect a sharp increase soon in the unemployment rate as the recession deepens. Recent actions by the Federal Reserve to tighten credit availability only make that prospect more certain, experts say.

For instance, Allen Gutheim, an economist with Wharton Economic Forecasting at the University of Pennsylvania, said the unemployment rate still is expected to reach 6.5 percent by the end of the year.

But increasingly, administration economists are scaling back how much impact they expect the recession to have on inflation. Last week Charles Schultze chairman of the Council of Economic Advisors, said the economy's underlying rate of inflation -- a concept that excludes the often wide and erratic swings in food and energy prices -- was now between 8 percent and 9 percent.

Yesterday COWPS director Russell said he expects that underlying rate to rise further during 1980.

In contrast to the basic survey of households, which showed unemployment dropping by 220,000 last month, a separate survey of actual company payrolls registered a 306,000 increase. The two surveys often do not move together month-by-month, but over the last four months indicate an almost identical increase in employment of more than 500,000.

But over that same period, the number of people either at work or looking for jobs has risen by almost 950,000, adding nearly half a million would-be workers to the ranks of the unemployed.

The employment increases shown in the payroll survey were concentrated in service-producing industries.