K mart Corp. says its income climbed 12 percent in the second quarter to a record $162.8 million despite slow growth in sales.

The rapidly expanding company, which owns the K mart discount stores, Waldenbooks, Pay Less Drugs, American Fare hypermarkets and other chains, said sales in the quarter ended July 27 rose 6 percent to $6.68 billion.However, sales on a comparable-store basis - a comparison of sales at stores that were open in the second quarter of 1987 - edged up 2.1 percent.

"While the sales increase in our K mart discount stores was fairly modest, we are encouraged by the results from two of our strategic programs," said Chairman Joseph Antonini.

"Our once-a-week advertising program is gaining momentum and giving new dimension to our various merchandising programs," he said. "We have been placing great emphasis on lowering shelf prices."

That strategy squeezed K mart's profit margin in the second quarter. The gross margin declined to 26.9 percent of sales from 27.2 percent in the corresponding 1987 period. The drop also reflects K mart's recently acquired controlling stake in the Makro club of warehouse-style stores, which sell deeply discounted goods to members.

Looking ahead, Antonini said, "We believe we will be seeing an improving retailing environment in the second half of the year and a continued strengthening of K mart's position in the marketplace."

At the end of July, K mart was operating 3,980 outlets.