Excluding fuel, like-for-like sales, which strip out the impact of new store openings, fell 1.1% in the 16 weeks to 24 September. Total sales fell 0.4%.
Despite the drop, the UK's second-largest supermarket said it was continuing to make progress.
Chief executive Mike Coupe said he was confident its strategy would enable it to "outperform our major peers".
German discount chains Aldi and Lidl, which have expanded rapidly in the UK, have been undercutting Sainsbury's and its rivals, including Tesco, Morrisons and Asda.
The supermarket chain has fought back by cutting prices on its everyday products rather than run promotions. This quarter, it said it had cut the prices of broccoli, onions, Margherita pizza and its own-brand nappies.
Mr Coupe said this strategy was working with customers "consistently choosing" Sainsbury's over its rivals.
He also said its £1.4bn takeover of Argos-owner Home Retail Group, which was completed at the beginning of this month, would speed up its plans to allow shoppers to get their goods in different ways.
Sainsbury's, which already has 15 Argos stores within its own shops, said it would open 200 digital collection points in its stores by the end of the year.
The supermarket group said Home Retail Group's like-for-like sales in the second quarter to 27 August, before it took over the firm, rose 2.3%.
In another attempt to win more shoppers, and amid the threat of online giant Amazon's move into grocery deliveries, Sainsbury's said it was expanding a test of its one-hour grocery delivery service in London called "Chop Chop" with orders delivered by bicycle.
The retailer said it would "give customers more options to shop with us whenever and wherever they want".
Sainsbury's has reported two straight years of falling profits, and analysts expect another drop in the 2016-17 financial year.
In May, the supermarket said underlying profits for the year to 12 March fell to £587m from £681m in the previous year.
Shares in the group have fallen 9% over the past six months.
John Ibbotson, director of retail consultancy Retail Vision, said Sainsbury's simpler pricing strategy and abolition of multi-buy promotions was "distinctly underwhelming" in the current brutal market conditions, but said Argos could help the firm.
"Argos should boost Sainsbury's bottom line in the short-term as well as improve its internet offer and logistics capability.
"But integrating the two firms will be time-consuming and distracting, and in the current environment Sainsbury's cannot afford to take its eye off its core grocery business, even for a second," he added.
Earlier this week, discount rival Aldi showed it was not immune to the effects of the continuing price war, with low prices eating into its profit margins. The firm reported a 12% rise in sales for 2015, but said operating profits had fallen 1.8%.
Sainsbury's has reported a second consecutive quarter of falling sales, blaming falling food prices.