The nation's civilian unemployment rate last month remained unchanged from July's 7.5 percent as the creation of new jobs slowed dramatically, the government reported yesterday.

The number of people employed in August dropped by 425,000, following monthly increases averaging 469,000 from January through May, the Labor Department said. However, another and usually more reliable measure of employment showed a small gain of 159,000 jobs.

The jobless rate fell sharply in June, from 7.5 percent to 7.1 percent, then bounced back in July to 7.5 percent, the rate prevailing when President Reagan took office.

The White House, which has boasted of the economy's record-breaking growth during the beginning of the economic expansion, said the August unemployment figures were "encouraging" because they remained stable.

The Reagan administration and many private economists have said they hoped economic growth would slow somewhat from its rapid pace earlier this year to prevent an acceleration of inflation that would cut short the expansion.

"It's clear the economy is capable of producing long-term prosperity," said White House spokesman Larry Speakes. "The dramatic economic growth of the last six quarters is moderating to a degree that promises lasting improvement in employment, inflation and other aspects of the economy. The more than 6 million new jobs created since November 1982 are a billboard for that future."

In a separate report, the Labor Department said the unemployment rate in the District in July rose from 8.9 percent to 9.0 percent. Unemployment in the metropolitan area also increased, from 4.1 percent to 4.2 percent. D.C. officials blamed an increase in the size of the labor force for the rise in the jobless rate.

Labor Department economists said last month that the sharp rebound in the national unemployment rate for July could have been caused by problems in adjusting the numbers for seasonal fluctuations.

Yesterday, the department said the seasonal-adjustment factor again may have been at work. Janet L. Norwood, commissioner of the Bureau of Labor Statistics, said that the employment survey was taken later than usual last month, taking into account a larger-than-usual number of students who left jobs and returned to school.

However, Norwood also said that it seemed clear that the economy was slowing down. "The unemployment data for August, when taken together with those for July, suggest that employment growth has moderated from the rapid pace registered earlier in the recovery."

Some economists have suggested that the economy will slow so much that it will cause a growth recession -- an economic expansion too weak to keep unemployment from rising -- in 1985. Martin S. Feldstein, former chairman of President Reagan's Council of Economic Advisers, said in an interview earlier this week that while a growth recession isn't likely next year, it isn't impossible.

Most of the job growth last month, unlike that of previous months, reflected gains by blacks, whose employment increased by 185,000.

Economist Andrew Brimmer said that increase followed the traditional business cycle pattern of blacks being the last hired. "That's what we're seeing now," Brimmer said.

Lawrence Chimerine, chief economist for Chase Econometrics, said the economy was entering a new phase of moderate growth and that the nation's output should increase at about a 4 percent annual rate, following the 10.1 percent rate during the first quarter and a 7.6 percent rate in the second quarter.

The number of unemployed persons remained virtually unchanged last month from the 8.5 million level in July and in May. It had dropped slightly in June. The number of persons employed declined from 105.395 million in July to 104.969 million in August.

The hourly earnings index for production workers on private nonagricultural payrolls declined slightly from July to August and has risen slowly from the beginning of the year, suggesting that wage inflation has been moderate.

Jobless rates for most major working groups were essentially unchanged in August, the Labor Department said.

The rate for adult men declined from 6.5 percent to 6.4 percent, that for women rose from 6.9 percent to 7.1 percent, and the rate for teen-agers rose from 18.3 percent to 18.4 percent, the Labor Department said.

The unemployment rate for whites was 6.4 percent and that for Hispanics was 10.7 percent, both unchanged from July.

The unemployment rate for blacks edged down to 16 percent, the May level, from 16.9 percent.

The unemployment rate including persons employed in the armed forces in the United States also was unchanged from the July rate of 7.4 percent.

The Labor Department measures the unemployment rate using a survey of households. However, it also polls businesses in a separate survey that economists say tends to be more accurate. It was the survey of businesses that showed that the number of jobs increased by 159,000 last month.