Mike Coupe told an audience at Mumsnet conference Mumstock that the discounters were "increasingly looking like conventional supermarkets, with all of the attendant costs".
The biggest barrier for us to overcome is the price difference between the discounters and the major supermarkets, although that’s come down a lot in the last couple of years
Both German retailers have evolved their offers in an effort to reach more ABC1 consumers, with Lidl, for example, introducing an extensive French wine range.
Both supermarkets have also retooled their marketing in the last year to emphasise the quality of their products. Lidl’s £20m ‘Lidl Surprises’ campaign showed real consumers trying the supermarket’s items at a farmer’s market and being surprised by the quality.
But Sainsbury’s, Coupe said, had managed to reduce prices while still stumping the discounters on range and convenience.
More than just price
His rivals have put out similar comments in the last week. Also speaking at Mumstock, Asda boss Andy Clarke said conventional supermarkets could provide an "everything under one roof" service in a way that the discounters could not, due to their limited range.
Tesco CEO Dave Lewis made similar comments last week, saying that customers wanted range, service, availability and price – but "not just price".
"Aldi only have 2500 products," Coupe said. "The reason that even today the discounters only have 10% of the UK market is because many people shop a much, much larger portfolio of products.
"The biggest barrier for us to overcome is the price difference between the discounters and the major supermarkets, although that’s come down a lot in the last couple of years. And you’ve seen the growth of the discounters slow quite dramatically in the last year."
The supermarket boss spoke as his company celebrated its first sales growth in two years.
Like-for-like sales in the nine weeks to 12 March squeaked up 0.1%, while total sales excluding fuel grew 1.2%.
Sainsbury’s is also now facing a decision on whether to make a higher offer for Argos owner Home Retail, after its previous bid of £1.3bn was trumped by South African retailer Steinhoff by £100m.
"Our strategy involves knowing our customers better than anyone else, and being there for them whenever and wherever they want," Coupe said.