Tesco launched the offer last week displaying signs in all its stores in Sainsbury's corporate colours. Sainsbury's chief executive Sir Peter Davies confirmed he had ordered thousands of extra coupons to be sent to shoppers in areas with a high density of Tesco stores.
Tesco launched the push partly in response to the launch of Sainsbury's new loyalty card Nectar, which the supermarket group launched with BP, Debenhams and Barclaycard.
Davis told The Times that Tesco's offer would "cost them more than they think". A Tesco spokesman said Sainsbury's move was "pretty desperate" but it would honour the coupons in good faith.
The share prices of all the big chains have fallen sharply over the last six months and the coupon war is likely to increase competition in the run up to Christmas, further dampening shareholders' expectations.
Sainsbury results out last Friday bucked the trend, showing sales growth of 2.5% in the second quarter. Sainsbury's shares - which had fallen by more than 16 per cent over two weeks as a series of fears about profitability had emerged - rose 29p on Friday to 282p.
Shares in Somerfield, the UK's fifth largest supermarket chain, plunged 42 per cent on Monday after the retailer announced it was parting company with its chief executive Alan Smith.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the .