Sainsbury's has reported a 1.7% fall in like-for-like sales over the key Christmas quarter and warned that its outlook remained "challenging".
Chief executive Mike Coupe said a fall in food prices was likely to continue.
But he said the performance in the third quarter, covering the 14 weeks to January 3, showed an "improving trend". Sales had dipped 2.8% in the second quarter.
Sainsbury's said it enjoyed a record-breaking week before Christmas with 29.5 million customer transactions.
Mr Coupe said: "Sainsbury's has provided a great Christmas for our customers. Food price deflation and falling fuel prices have enabled our customers to treat themselves over the festive period."
But he added: "The outlook for the remainder of the financial year is set to remain challenging, with food price deflation likely to continue."
More price cuts
It comes as the supermarket announces its latest round of reductions as part of a £150 million investment in price-cutting announced last November.
Mr Coupe said: "Our performance showed an improving trend quarter-on-quarter.
"However, given the uncertainty in the trading environment, food price deflation and the price reductions we announced this week, we currently expect our fourth quarter like-for-like sales to be similar to that of our first half."
Mr Coupe said: "Our prices versus our supermarket peers have never been better."
He told Sky News that Sainsbury's had sold "the same amount of stuff we sold last year, but the prices were lower".
The update comes during a key week for the retailers announcing Christmas trading figures, with Tesco and Marks & Spencer due to disclose sales numbers tomorrow.
Supermarkets are engaged in a fierce price war amid a squeeze on their market share by discounters Aldi and Lidl while upmarket food offerings from Waitrose and M&S are also doing well - with Waitrose yesterday reporting a 2.8% Christmas sales rise.
Sainsbury's own high-end range, Taste the Difference, did well over the third quarter with growth of 5%, including prosecco sales up 30%. It also sold more than 57 million mince pies and more than 550,000 turkeys, up 8% year-on-year.
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