House prices in the District rose by an average of only 7 percent during the first three months of this year, the smallest jump in five years and an indication that the torrid real estate market has begun to cool.

Compared with the first quarter of 1979, city records show that sales were down by 9 percent; compared with the boom year of 1978, sales were down by 30 percent.

The District's real estate assessment office reports that a handful of the city's 57 assessment neighborhoods had large price increases on average during the first quarter of 1980, but the overall pattern was one of moderation.

In high-priced Georgetown, prices rose by 25 percent, from $233,000 in the first quarter of a year ago to $292,000 this year. In each period, 25 houses were sold.

Prestigious Spring Valley in far Northwest, however, had an 8 percent decline in its average sales price, from $237,000 to $218,000, with only five sales reported in the first three months of this year.

The overall average price for homes in the District, excluding condominiums and cooperatives, rose from $86,000 in the first quarter last year to $92,000 this year. The slowdown in city-wide price increases, expected here for more than a year because of high mortgage interest rates and tight money, also reflects a growth in the number of sales in Southeast and Northeast.

Neighborhood statistics compiled by senior residential assessor George B. Altoft reveal that while the number of sales in the higher-priced areas of Northwest have been flat or declining during the past year, there has been a big surge in sales in Congress Heights (up 70 percent over 1979), Hillcrest (up 43 percent), Marshall Heights (up 200 percent), Deanwood (up 61 percent) and Brookland (up 24 percent).

Total sales in the nine assessment areas of the city east of the Anacostia River went from 90 in the first three months of 1979 to 197 during the same period this year, a gain of nearly 120 percent.

However, west of the Anacostia on Capitol Hill -- one of the most active real estate markets in the city for four years -- house sales dropped by 40 percent between early 1979 and 1980, from 52 transactions to 31. Even larger declines were experienced in some of the nearby, highly speculative areas on the fringes of the Hill, such as Capitol East.

The new sales figures indicate that 13 of the 57 neighborhoods now have average home prices of $200,000 or more, up from 11 neighborhoods this time last year. Garfield, Wesley Heights and Crestwood -- all in the Northwest -- joined that luxury-price category.

Observatory Circle dropped out of that bracket as its average sales price decreased from $276,000 to $164,000. Berkley in Northwest had no sales in the first quarter; its average sales price was $217,000 in early 1979.

Twenty-eight neighborhoods in the city have average sales prices of $100,000 or more, while 21 have average prices under $75,000. Nine neighborhoods, virtually all in Southeast or Northeast, have average home prices under $50,000.