Unemployment in the District of Columbia and its surrounding area remained at record levels in July, according to figures released yesterday by the city's Department of Employment Services.

The unemployment rates of 11.4 percent for the city and 6.3 percent for the metropolitan area are virtually unchanged from levels recorded in June, when unemployment rose to its highest level since officials began the present method of record-keeping 12 years ago.

Recent high school and college graduates continued to account for a major share of the joblessness. In June, nearly 70 percent of those out of work were recent graduates, typical of the summer influx of potential new workers, officials said. But the situation this year also was affected adversely by cuts in the federal work force and a general slowdown in the nation's and the area's economy.

Fewer people who had been claiming unemployment benefits were able to find work in July, officials reported. Those jobless remained so, on the average, nearly 23 weeks.

Overall, there were 6,300 more persons unemployed in the District than in July 1981, while there were 9,600 more people out of work in the suburbs than a year ago.

Matthew F. Shannon, acting director of the employment services department, said July figures for Washington "follow the national trend." Normally, Shannon said, the area's economic base grows by about 2.8 percent each year, but growth this year is only about half that rate.

According to the July statistics, there were 109,800 unemployed persons in the metropolitan area's work force of about 1.75 million.

Of those, 38,500 were District residents, an increase of 2,600 from the previous month. The city's unemployment rate for June was 11.3 percent.

In the rest of the metropolitan area, there were about 71,300 persons out of work in July, 2,500 fewer than the month before, when unemployment was 5.2 percent.

The last time the city's unemployment rate approached the current level was in June 1973, when it reached 11.1 percent. The previous high metropolitan rate of 6.1 percent was recorded in February of this year. Figures published before 1970 were compiled differently and are not directly comparable to current statistics.

Employment in July was up marginally in general merchandise trades, apparel and accessories, restaurants, banking and business services.

"Those are small gains," Shannon said, "but they are significant in that the same areas reported losses before. It shows that hopefully the private sector has bottomed out."