Sainsbury's said like-for-like sales fell 1.7% in the 14 weeks to January 3 and boss Mike Coupe said the outlook remained "challenging".
He said a fall in food prices was likely to continue, but said the performance in the third quarter 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.
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.
The outlook for the remainder of the financial year is set to remain challenging, with food price deflation likely to continue.
Sainsbury's has said it will reduce spending on new stores and look into more cost-saving methods to help finance price cuts in an effort to cope with the toughest market conditions for decades.
Sainsbury's posted a profit before tax and one off items of £375 million for the six months to 27th Sept. This figure is ahead of analysts' expectations of about £350 million, but down from £400 million in the same period last year.
Sainsbury's has apologised after a lesbian couple were asked to stop kissing in one of their stores - on National Coming Out Day.Read the full story ›
Discount supermarket Netto is set to return to the UK as part of a joint venture with Sainsbury's that will take on rivals Aldi and Lidl.Read the full story ›
These are "very challenging times for the grocery industry" but Sainsbury's is doing well against its immediate competitors, according to the supermarket's outgoing chief executive.
Justin King told Good Morning Britain Sainsbury's was still "growing a lot stronger than our grocery competition" and the whole industry was dealing with low growth.
Outgoing Sainsbury's chief executive Justin King says customers are "spending cautiously" as the supermarket chain posted a fall in sales in his final quarter before departing.
Throughout the quarter we have continued to invest in reducing prices and improving quality, increasing the value of our offer. Lower food price inflation and reduced fuel prices are a welcome respite to customers’ finances but they continue to spend cautiously, leading to industry growth in the quarter being the slowest in a decade [...]
We remain confident that our clear strategy and differentiated offer will allow us to continue to outperform our supermarket peers through the remainder of the year.
Sainsbury's like-for-like sales including fuel fell 2.4% in the first quarter of 2014, according to the company's trading statement.
Like-for-like sales excluding fuel were down 1.1%.
Total retail sales at Sainsbury's were up 1% in the first quarter of 2014, the supermarket has announced.