The District of Columbia's seasonally adjusted unemployment rate rose from 10.2 percent in June to 10.6 percent in July despite the recovery and the drop in the national unemployment rate, the D.C. Department of Employment Services announced yesterday.

The metropolitan area's jobless rate, which is not seasonally adjusted, fell slightly from 5.1 to 5.0 percent.

The national rate was 9 1/2 percent in July and in August.

"The overall trend in employment is not down in the District. It is actually an increase," said Ed Meyers, of D.C.'s employment service department.

The economic recovery nationally has been led by the manufacturing sector, but only 2.2 percent of city workers are employed in manufacturing compared with the national average of 21 percent, he said.

Some of the city's discouraged workers, who gave up the search for jobs and no longer were counted in the unemployment statistics, are actively seeking work again because of the recovery and are adding to the unemployment figures as well.

The number of federal jobs in the city declined by 19,600 between July 1980 and July 1983 and now stands at 215,500, and the cuts increased the number of those unemployed, Meyers said.

A coincidental factor in the District's unemployment is the "massive disinvestment of the federal government away from cities," he said. About half of the cities in a sample of 24 representative cities throughout the country are not participating in the recovery, he said.

Meyers said that city officials are "hopeful" the unemployment rate will fall before the end of 1983. During the last two recessions, the recovery reached the District several months after it began nationally, he said.

A positive sign is the 12.9 percent decrease since July 1982 in the number of workers filing claims for unemployment compensation, the city said.

The jobless rate, before seasonal adjustment, hit 11.3 percent in July, up from 11.0 percent in June. Although the number of district jobs actually grew by 4.8 percent in June, an influx of student and seasonal workers increased the labor force by 5.2 percent.

The Mayor's Summer Youth Employment Program contributed significantly in lowering the number of youths without jobs this summer. Without the program, which employed more than 18,000 young people, the jobless rate would have topped 14 1/2 percent in July, DOES estimates.