BJ's is working to turn around its business after facing disappointing sales and declining customer traffic in recent years. Last year, it took charges for closing its two ProFoods restaurant supply locations and shutting in-store pharmacies.
Zarkin told CNBC that its biggest challenge is increasing sales of non-food items such as apparel, furniture, and lawn and garden products.
"We've had great luck and great support in the television business and the electronics business, but where the discretionary income is going to be tighter for most of our consumers, we're going to have to make sure that we're extra-specially priced...to take advantage of the consumers that are shopping us for their basic needs," he said.
As part of its turnaround plan, BJ's has been reducing the number of items that it offers, and is stocking merchandise that either has better margins or sells faster.
Sales in the quarter rose almost 2 percent to $2.4 billion.
Its February comparable store sales rose 5.9 percent, including the effects of higher gasoline prices. On that basis, analysts, on average, were expecting a rise of 4 percent.
Demand was strong for juices, frozen foods, health and beauty products, meat, prepared foods, TVs and toys, it said, but weaker for apparel, cigarettes, furniture, tires and wine.
It expects comparable sales to increase by 1 percent to 3 percent in March, and by 10 percent to 12 percent in April.
BJ's shares rose $3.28 to $36.56.
Big Lots Shares Up
Big Lots is also in the midst of turnaround effort that has involved closing stores and revamping its merchandise. After acknowledging it strayed from its close-out roots, it is focused on getting existing customers to buy more in its stores, which has helped boost results.
Net income for its fiscal fourth quarter, ended Feb. 2, fell to $92.02 million from $104.3 million a year earlier. But earnings per share rose to $1.04 from 94 cents per share, helped by a buyback that reduced outstanding shares.
Excluding a bankruptcy settlement, Big Lots reported income from continuing operations of 93 cents per share, compared with analysts' average forecast for earnings of 84 cents, according to Reuters Estimates.
Its gross margin rate fell 0.8 percentage point, hurt by markdowns, but expenses decreased, helped by lower insurance costs and lower bonuses.
For the first quarter, it expects comparable store sales to rise 1 percent to 2 percent, and income from continuing operations of 30 cents to 35 cents per share.
Its shares rose $3.89 to $21.27.
--CNBC.com contributed to this report.