Giant Food Inc. admitted yesterday that its profits are being "substantially depressed" by the food price war it started last month.

The supermarket chain took the unusual step of announcing in advance that it will report much lower earnings when first-quarter profits are reported next month.

But Giant said its sales are running an estimated 16 percent ahead of last year -- an even bigger increase than industry analysts had projected.

Bigger sales were what Giant was shooting for when it announced April 5 that it would stop marking prices on individual items and slash the prices of 1,500 to 2,000 items.

Competitors responded to Giant's "warehouse pricing" by slashing their own prices, setting off a full-scale food price war.

Yesterday's announcement from Giant indicated the chain is winning the war for a bigger share of the food business, but so far losing the battle for profits.

The 16 percent sales increase reported by Giant apparently indicates that Giant is not losing business because consumers object to the removal of prices from individual grocery items. Giant was the first major food chain in the country to equip all its stores with electronic "scanners" that identify products from the striped Universal Product Code on the package, then extract the price from a computer.

Giant contends the money saved by not marking prices permits it to charge lower prices than competitors, which do not have scanners in all their stores.

But the major competitors also cut their prices, and none of them will say if they are losing business to Giant.

Giant officials would not disclose how much their profits have been hurt. They said earnings for the 12 weeks ending May 23 would be "substantially depressed compared to the prior year's same 12 weeks."

That quarter of 1980 was not a good one for Giant, which was then in the midst of a "price freeze" also aimed at building sales. Profits during March, April and May 1980 dropped 22 percent to $3.35 million (69 cents a share.)

The Giant announcement provided hints that the 127-store chain might report earnings of as little as $1 million for the latest quarter.