Asda, which is owned by US grocery giant Wal-Mart, said sales at stores open more than a year were 1.6% lower in the third quarter, compared with the previous three months.
In the second quarter, sales rose 0.6%.
Asda's chief executive, Andy Clarke, said that despite the fall in sales, he was pleased Asda was gaining market share at a difficult time.
"A year ago we took clear action to address the changes in our market and implement a five year strategy to redefine value retailing. That is a long term strategy that won't be delivered overnight."
He said the company's focus on offering value for money and promoting internet shopping was working but that conditions in the market were very difficult.
"The last quarter has seen a shockwave go through our industry and others are starting to respond to the challenges they face. I expect that we will see another tough quarter and I'm under no illusions that the battle continues to rage."
Asda vies with Sainsbury's to be the UK's second largest supermarket after market leader Tesco.
In a briefing with journalists, Mr Clarke and his team dismissed what they described as "gimmicks" used by rivals to boost short term sales.
Asda's chief merchandising officer, Barry Williams, said he had never seen as many money-off vouchers in 25 years, likening several of Morrisons' promotions to quantitative easing.
"These are desperate measures," he said.
"You can win a quarter with a voucher... We're not immune from the turbulence, but we judge our performance over a much longer period of three to five years."
Yesterday Sainsbury's announced Â£150m worth of price cuts as part of its new strategy to win shoppers.
" It feels like a drop in the ocean. Our price gap is already double-digit with Sainsbury's," said Mr Clarke.
He also said Asda was continuing to close the gap with the discounters through its Everyday Low Prices strategy.
"We are pulling away from the other three. There are very clear winners and losers in our market. We can see we're a very clear winner," he said.
Sales at Asda have fallen, hit by what the retailer called "a shockwave" in the supermarket sector.