Retail sales began to pick up last month, raising hopes that a strong Christmas season will provide some of the fuel needed to power the nation out of recession.

Major department store chains catering to more affluent customers reported substantial gains, but discount store sales fell because lower-income customers are feeling the brunt of the recession.

"The sales increases look better than they have in several months," said Jeffrey Edelman, a retail analyst with the securities firm of Dean Witter Reynolds Inc. "There was an acceleration in the rate of gain.

"Retailers this year are a little more promotional with markdowns, creating some of the thrust. Stores have to push extra hard to make the sales."

The nation's largest retailer, Sears, Roebuck & Co., reported that its sales were up 4.9 percent to $1.81 billion. J. C. Penney & Co., ranked third, posted a 2.9 percent gain and No. 4 F. W. Woolworth Co. reported that sales climbed 4.3 percent.

K mart, the second largest retailer, and No. 6 Montgomery Ward were the only companies among the industry leaders to report sales drops.

Washington department store sales have been improving since summer and continued to be better than much of the country during November.

"Sales have been very strong. We had a good October and a good November," said Edgar Mangiafico, chairman of Hecht's, a division of the May Department Stores of St. Louis. May does not release separate results for Hecht's, but total company sales for the month were up 13.8 percent to $375 million from $330 million. Year-to-date sales rose 6.1 percent to $2.78 billion.

Mangiafico said Hecht's sales have been "better than the trend and better than we planned it to be." Like most retailers, Hecht's is advertising heavily and cutting prices "but not any more than we were last year," he added. "The promotional business is up, but all of the business is up proportionately."

Jeffrey Feiner, a retail analyst at the securities firm Merrill Lynch Pierce Fenner & Smith said, "Trends in retail sales in November showed some minor improvement from the lackluster pace of the last several months and as well as from the relatively sluggish pace experienced in November 1981."

Sears' sales for the four-week period ending Nov. 27 totaled $1.81 billion, compared with $1.73 billion in November 1981. For the year to date, Chicago-based Sears reported that sales rose 2.3 percent to $16.13 billion from $15.77 billion a year earlier.

Penney, based in New York, reported its sales last month rose to $1.05 billion from $1.02 billion in 1981. Penney sales for the 43 weeks ended Nov. 27 were up 0.7 percent to $8.25 billion from $8.20 billion.

New York-based Woolworth reported its sales for the four weeks ended Nov. 23 totaled $622 million, compared with $597 million in 1981. The company noted that the increase was partly caused by the big going-out-of-business sale at its Woolco discount stores. Woolworth reported its year-to-date sales rose 1.7 percent from $5.59 billion to $5.69 billion.

K mart, which is based in Troy, Mich., reported that November sales dropped 3.8 percent to $1.38 billion from $1.43 billion a year ago.

Edelman said K mart's poor results were caused by two factors: that its customers are mostly lower income and Midwest consumers, who have been especially hard hit by high unemployment and the recession, and by the fact that the report includes sales only up to Nov. 24, short of the Thanksgiving weekend.

K mart sales for the year were up a slim 1.6 percent to $13.01 billion from $12.81 billion.

Here are results for the other big retailers:

* Federated Department Stores Inc., No. 5 and based in Cincinnati, reported a 10.2 percent gain in November to $607 million from $551 million a year ago. For the first 10 months of 1982, the retailer reported sales rose 8.2 percent to $4.86 billion.

* Montgomery Ward, the Chicago-based subsidiary of Mobil Corp., had a 0.5 percent slip to $530 million from $533 million. So far this year, sales are down 3.4 percent to $4.38 billion.

* Dayton Hudson Corp. of Minneapolis, No. 7, posted the largest gain in November, with sales rising 14.2 percent from $448 million to $512 million. Dayton Hudson, which has done the best all year, reported that its sales for the first 10 months were up 13.9 percent to $4.15 billion.

* May Department Stores, ranked eighth and based in St. Louis, posted a 13.8 percent gain to $375 million from $330 million.