Gamble-Skogmo Inc., a Minneapolis retailer, is trying to buy a major and potentially controlling block of stock in Garfinckel, Brooks Brothers, Miller & Rhoades Inc., the big Washington retail chain revealed late yesterday.

Garfinckel's said the company "has been advised that Gamble-Skogmo may be attemting to purchase, at a premium, blocks representing approximately 20 percent of Garfinckel common shares."

Pursuing the usual defense tactics when an unwanted take-over bid is made, Garfinckel warned that "it would violate the antitrust laws if Gamble were to acquire control of Garfinckel" and charged that, "the manner in which Gamble may be attemping to buy Garfinckel shares apparently violates other federal and state laws."

Garfinckel executives refused to go beyond the company's carefully worded statement. Gamble-Skogmo officials refused even to acknowledge they were interested in Garfinckel.

Garfinckel's statement said Gamble-Skogmo had made offers for about 20 percent of the company's stock to "certain (share) holders, including a director of Garfinckel.

The only Garfinckel director who controls enough stock to play a significant role in a take-over is Joseph R. Harris. Jr., former Chairman of the Joseph R. Harris retail chain, now owned by Garfinckel's.

Harris himself owns 138,468 shares. And along with 26 other former Joseph R. Harris Co. shareholders, the former chairman controls a total of 483,235 shares, about 10.7 percent of the 4.5 million outstanding shares. No other persons own more than 10 percent of the stock, the company's 1978 proxy statement shows.

Harris could not be reached for comment yesterday. Although the Harris family shares are enough to assure a seat on the Garfinckel board of directors, the family's influence was not strong enough to keep two Harrises from being outsted as heads of the Harris chain last year.

J. Robert Harris III, who had been president, and Donald Harris, executive vice president, were replaced by Stephen Spiro, a young merchant hired away from Bloomingdales.

The Harris women's wear stores are the only link in the Garfinckel chain that the company admits is unprofitable. In an attempt to regain profitability, the chains were remerchandised for the Fall season and last month the Joseph R. Harris name was discarded in favor of Harris and Friends.

Despite the problems at Harris, the Garfinckle's chain reported a 135 percent increase in profits for the second quarter of 1978. Earnings jumped from $385,000 to $903,000 as sales increased from $68 million to $86 million for the three months ended July 29.

David Waters president and chief executive has predicted the chain's 1978 earnings will top $3 a share - up from $2.61 in 1977 - and sales will climb from $330 million to $400 million.

In addition to the Harris, Garfinckel and Brooks Brothers stores in Washington, the company runs the Miller & Rhoads department stores, headquartered in Richmond, Miller's department stores in Tennessee and Harsfeld's in Kansas City.

Under an acquisition program launched by Waters to boost earnings and profits, the company last year acquired the Ann Taylor chain of high fashion women's shops and Catherine's Stout Shoppes.

Gamble-Skogmo is a bigger - sales of $1.6 billion - and even more diversified retailer. Founded by Bertin C. Gamble, who retired last week at age 79, the company began as a chain of midwestern auto supply stores called Gamble's and now has 30 divisions in the United States and Canana.

Despite its size, Gamble-Skogmo last year earned less profit than Garfinckle, turning in earnings of $9.8 million in contrast to Garfinckel's $11.2 million net.

In contrast to Garfinckel's emphasis on high priced soft goodS, Gamble's is mostly a mass marketing hard goods operation.

Last June Gamble-Skogmo paid $29 million in cash and notes to acquire control of Howard Brothers, a 79-unit chain of descount stores based in Monroe. La.

Gamble's bid for Garfinckel is th third major takeover fight this year involving a publically owned Washington company.

(Contributing to this story was Washington Post Special Correspondent Austin Wehrwein.