Asda, which has 17 stores in Northern Ireland, has posted its worst decline in quarterly sales for many years, as it reported a 3.9% slump at the start of this year.
The accelerating decline, after a 2.6% fall at the end of 2014, comes amid a fierce supermarket price war as Britain's biggest grocers see their market shares eaten away by Aldi and Lidl.
Chief executive Andy Clarke said: "It's been some time since we have seen that level of decline."
He said the scale of the fall had previously been seen "in the early days of Asda" but pointed to the wider context of the struggling market.
"It is clear that the big grocers are losing market share and that the discounters are continuing to grow. As expected, the market remains turbulent. Customers are preferring to save."