Giant Food Inc., the dominant supermarket chain in the metropolitan area, is becoming an increasingly important player in the drugstore industry as well.

While still a distant fourth -- behind Peoples Drug Stores Inc., Dart Drug Stores Inc. and Gray Drug Fair -- Giant had the largest growth in market share of any of the local drug chains last year, according to figures released last week by Chain Drug Review.

Giant, which accounts for 42 percent of all grocery sales in the area, rang up 8.9 percent of all local drugstore sales, up from the 7.5 percent market share it had in 1983. The other chains reported only marginal changes from 1983.

Giant's gain comes after an intensive marketing campaign begun last summer, when the chain announced price cuts of 10 to 30 percent on a wide assortment of items. Giant's move triggered a price war among area drugstores.

The price cuts also led to a drop in Giant's profits, but the company vowed to continue offering the bargains because, a spokesman said, "the whole idea is to increase sales volume."

The fact that other major chains are holding their own in terms of market share means that Giant's increase "came at the expense of the independent drugstores," said David Pinto, editor of Chain Drug Review.

According to the publication, Peoples is still the market leader. It had 26.8 percent of all area drugstore sales last year, down slightly from 26.9 percent in 1983.

Peoples Chairman Sheldon W. Fantle disputed the 1984 figures, saying "we figure that our share is 31.6 percent."

Chain Drug Review said Dart is the area's second-largest chain, accounting for 26.1 percent of sales -- a marginal increase from 25.9 percent in 1983.

Gray Drug Fair stayed at third, with a 21.9 percent market share -- up slightly from its 21.6 percent share in 1984, but below the 23.5 percent share it enjoyed before Drug Fair was sold to Cleveland-based Gray Drug Stores Inc. in 1981.