A handful of little-known discount food stores, popularly known as "box stores," has appeared on the fringes of Washington recently, triggering a wave of price reductions at nearly 300 area supermarkets.

Giant and Safeway, which control 60 percent of the local market, have slashed prices on some items by as much as 37 percent. Both are trying to counter low prices at the new No Frills store in District Heights and at similar box stores here.

Five such stores, called Plus Discount Food Stores, have been opened in the last few days. A&P supermarkets and Grand Union, the other major chain stores here, have not joined the most recent pricecutting movement.

The new stores cut their own costs by offering few fresh, frozen or refrigerated products and few of the usual amenities of a major supermarket. They generally do not accept checks, do not stamp prices on the individual items they offer and do not bag purchases. They carry few different brands of the same item, and customers pack purchases in bags they bring themselves or in boxes that sometimes are available at the stores.

Jim Scott, manager of No Frills here, said his prices "were 30 percent lower than [the majors] were on everything, but since they cut prices, we are both about the same."

A comparison of the No Frills price list and Giant and Safeway newspaper advertisements announcing price cuts showed the majors now have the same or nearly the same prices on several dozen products.

No Frills is still lower on catsup at 69 cents for a 32-ounce bottle, despite Giant's 37-percent price cut from $1.25 to 79 cents.

The two have identical prices on corned beef -- $1.19 for a 12-ounce can -- which is down 31 percent from Giant's regular price. Both offer bread at 29 cents for a 22-ounce loaf.

Giant undercut its new competitor on Cheerios cereal by lowering its price for a 15-ounce box by 23 percent to 99 cents, compared with $1.09 at No Frills.

"I wouldn't describe this as a price war, but anything could happen," said Ernest Moore, manager of public affairs for Safeway, which has marked down its prices about as much as Giant.

"But they have reduced prices only temporarily," protested Scott, who said two No Frills stores have opened in Baltimore and two more are planned for the Washington area. "They want to stop us from growing, and if they can push us out, they will raise their prices back up again."

Giant's ad said, "These 'no frills' stores try to attract customers by claiming that they offer lower prices." But with the Washington-based chain's price cuts, the ad said, customers "don't pay a premium to shop with us."

A Grand Union spokesman said his company is watching developments in Washington while experimenting with a box store in Sunrise, Fla. He added that Grand Union executives consider the discount grocery stores one of "the dominant forces of the 1980s in meeting the needs of consumers."

Plus Discount Foods, which has opened outlets in Fairfax, Vienna, Woodbridge, Suitland and Severna Park, is a wholly owned subsidiary of A&P.

Scott said his company entered the Washington food market "because the prices here are so high." The metropolitan area has often outpaced the nation in the rising food prices measured by the U.S. Labor Department's Consumer Price Index.

At No Frills yesterday, shoppers crossed picket lines thrown up by the Retail Store Employees Union.

Max McGhee, a union representative, said the store owner had refused to allow the union to represent the clerks working at No Frills.

Among the customers shopping inside was the Don Campbell family.

"Our insurance man told us about this place," said Campbell, a government painter who had accompanied his wife and daughters to the store. "It is a lot cheaper. Two cans of evaporated milk here cost 70 cents; they are 89 cents at the supermarket."

The Campbells drove six miles from their home in Oxon Hill to shop at the new store. "We figured out the gasoline cost and we still save money by coming here," he said.

The District Heights store is in an old warehouse with a new coat of chocolate brown paint. The floor is covered with plain green-and-white linoleum.

Instead of displaying merchandise on shelves, the store has rows of stacked cardboard boxes. Shoppers select their purchases of canned goods and packaged goods directly from the "box" stores.

No Frills insists on cash or food stamps in payment for groceries.

The box store sells almost no perishables such as fresh meat, produce, dairy or frozen foods.

"We have 450 items, usually one private brand or one generic brand and only one size," Scott said.