Unemployment in the metropolitan Washington area dropped to a four-year low of 4.4 percent in June, but unemployment in the District jumped to 8.4 percent, the D.C. Department of Manpower reported yesterday.

The 8.4 percent unemployment rate for the city was up sharply from the 8 percent reported in May, while the unemployment rate for the overall area was down slightly from 4.5 percent in May.

Unemployment in the metropolitan area has been falling generally since February 1977, when the rate has been increasing since March of this year, when it was 7.6 percent.

The June unemployment figures reflect a continuing trend of new jobs being created in the suburbs with every little growth in the city. In June, for example, employment increased by 20,100 jobs in the suburbs but by only 200 jobs in the city.

While the number of jobs increased, the number of people looking for jobs also increased sharply in June.

Nationally, the unemployment rate was 5.7 percent in June.

The employment situation has improved here since June 1977, when the metropolitan area unemployment rate was 5.3 percent and the rate for the District was 11 percent.

Lately, however, the D.C. unemployment rate has been climbing sharply since after falling briefly at the start of the year, District unemployment has been rising since March. The overall unemployment rate for the whole metropolitan area has been steadily decreasing since January, when it was 5.1 percent.

Since June 1977, total employment in the city has increased by only 300 jobs, while in the whole metropolitan area employment has increased by 29,500 jobs.

In June, total area employment increased by 15,800 jobs, with the largest increase - 4,000 jobs - occurring in both government and the construction industry.