Supermarket prices in the Washington metropolitan area rose 0.3 percent last month compared with an average 1.1 percent rise in all American cities, the Labor Department reported yesterday.

The relatively modest increases here in December followed declines of 0.3 percent during November and 0.4 percent for October -- adding up to an unusual, three-month respite from soaring grocery store prices, which has been attributed to the introduction of "no-frills" food outlets as competitors to the area's major chains.

But market inroads by "no-frills" stores -- which feature discount prices on a smaller variety of goods, often sold from stacks of boxes -- developed only in the last months of the year after prices had soared in the Washington area.

Thus, for 1979 as a whole, area grocery store prices still rose 9 1/2 percent -- the same figure as for the national city average price inflation. In effect, food store prices elsewhere in the country increased more slowly early in the year but continued to rise when area prices reached a plateau.

More than a dozen of the so-called "box" stores opened here last year -- nine of them plus units of the Great Atlantic & Pacific Tea Co., which also operates regular A&P supermarkets here -- and about two dozen of the new stores are expected to be in business by mid-1980, almost all of them in the Maryland and Virginia suburbs.

Giant Food Inc., the largest area food retailer, has countered the competition by reducing food prices on a limited number of products -- but only at stores close to the new competitors, so not all area consumers are benefiting from the price wars of some neighborhoods. A Giant spokesman said yesterday the "experimental" price-cutting is continuing at selected stores, although Giant in earlier years had vowed to have uniform prices at all its area outlets.

According to the Labor Department, prices of cereal and bakery products rose 1.6 percent last month and meats, poultry, fish and eggs increased an average 1.4 percent at areafood stores, accounting for the overall higher prices.

Fruits and vegetables declined 1.4 percent during the month, with prices for most fresh vegetables higher but prices for most fresh fruits down substantially. In particular, the government reported, prices rose for pork, beef, bread, poultry and eggs while prices fell for cola drinks, roasted coffee and lettuce.

The Labor Department's Bureau of Labor Statistics gathers information monthly on area food store prices. Overall consumer price index data for the D.C. area is compiled every other month; the next such report, for January, will be published in a month.