The number of reported crimes in the United States dropped by 5 percent in the first six months of 1982 compared with the same period last year, the FBI said yesterday. It was the first decline in four years.

But while crime was decreasing in most big cities, figures for the District of Columbia showed an increase of almost 3 percent overall.

The FBI's figures, which are released twice a year, showed that violent crime was down 3 percent across the nation while non-violent crime decreased 6 percent.

Although the statistics were encouraging, law enforcement officials cautioned against attaching too much importance to them.

Attorney General William French Smith noted that reported crimes had reached an all-time high in 1980 and remained at that level through 1981.

"While this apparent reversal is encouraging, the fact that the all-time high was reached and maintained for a two-year period should be a major concern to the nation," Smith said.

FBI Director William H. Webster added, "This drop in reported crime is the first six-month decrease the nation has experienced since 1978. In that year, we had a 2 percent decrease."

The law enforcement officials said they could not provide any definite explanation for the recent decline, but the FBI's uniform crime report for 1980 pointed out that 70 percent of all crimes are committed by persons who are under 21 years of age. The number of people in that age group has declined in recent years.

The FBI's nationwide study found that murder was down 8 percent, robbery down 7 percent and rape down 6 percent. The only increase in violent crime was for aggravated assault, which went up by 1 percent.

Changes for other crimes for the country as a whole included these: burglary down 11 percent, and larceny and motor vehicle theft down 3 percent.

Geographically, the Northeastern and North Central sections of the country experienced the greatest decline in crime, 9 percent, while crime decreased by 2 percent in the South and 3 percent in the West.

In the District of Columbia, the number of murders stayed almost constant (102 in the first six months in 1982, 103 in 1981); rape increased by more than 9 percent; robbery decreased by 5 percent; aggravated assault was almost constant; burglaries were down almost 6 percent; larceny and theft increased more than 9 percent, and motor vehicle thefts were up more than 14 percent.

Nationally, cities with more than a million population had a 5 percent decrease in violent crime and a 1 percent increase in property crime. In rural areas, crime was down 11 percent, and in suburbs it decreased 8 percent. Cities of more than 50,000 population had an overall decrease of 3 percent