The "warehouse prices" supermarket war that started in April smashed Giant Food Co.'s first-quarter profits, Washington's biggest food chain reported yesterday.

Giant's earnings dove 94.7 percent from $3.3 million (69 cents a share) to $176,000 (4 cents), resulting in Giant's least-profitable quarter in a decade.

Profit margins were squeezed so thin they had to be measured in thousandths of a percent; Giant's earnings amounted to 0.048 percent of sales.

That means the company kept only 48 cents of every $1,000 rung up by its electronic cash registers, instead of the $12,50 to $15 Giant usually earns on each thousand dollars worth of groceries it sells.

Giant officials blamed more than three-quarters of the drop on the one-time cost of starting the new marketing strategy that set off the supermarket price war.

On April 5, Giant announced it no longer would mark prices on individual food items but would depend totally on its computerized electronic scanners to read the striped labels on cans and boxes.

To head off consumer backlash against the end of item pricing, Giant announced sharp reductions in the price of more than 1,500 staple items and launched a new advertising program touting its "warehouse prices."

The morning after Giant fired its shot, Safeway retorted with its own price-cutting program but promised to keep the prices marked on individual items. Other supermarkets quickly responded in an effort to keep from losing business.

Giant, however, appears to be winning the competition for customers.

Sales for the three months ended May 23 jumped to $362.6 million from $313.9 million in the first quarter of 1980.

The gain amounted to 15 1/2 percent, but Giant said its volume gains are actually higher. The quarter was half over because the new marketing strategy started, so the impact on a full quarter's sales isn't known yet.

Because the selling price of a significant number of items was cut dramatically, the increase in the number of cases of merchandise sold was more than 15 1/2 percent. The company said measures of tonnage shipped from distribution centers and customer transactions per store "have generally shown increases."

Giant has been increasing its share of the Washington food dollar steadily for more than a year and now is estimated to account for 37 percent of supermarket sales in the Washington area, up more than three percentage points in the past year.

In announcing what it acknowledged were "substantially depressed" earnings, Giant insisted the gain in sales shows that the price-cutting program was "right on target."

The announcement said "the trend is positive" and "Giant will continue to promote its warehouse pricing program agressively."

The company said, however, that it "is not yet in a position to make a prediction as to when earnings will return to historic levels."

It cost Giant about $2.5 million to launch the warehouse-pricing campaign, including overtime pay for marking down prices, the cost of printing and installing bigger shelf price signs and heavy advertising.

The cost savings Giant expects to gain from eliminating item pricing "only are beginning to take effect," the company said. Union contracts prohibit laying off workers because of automation, but as job come open Giant is filling them with workers who formerly marked prices on products.