Morrisons cut the price of more than 5,000 key items earlier this week as part of its reaction to the rise in VAT to 20%.
Focusing on "typical" baskets of shopping, Morrisons said it would reduce the cost of 44 items from £96 to £56.73.
Morrisons aims to compete on price and Asda has traditionally been the cheapest of the major supermarkets.
Asda has responded by undercutting competitor prices by 10% using its Asda Price Guarantee scheme, in association with mysupermarket.co.uk.
Until now, Asda guaranteed the cost of its customer's shopping was cheapest in its stores by refunding the difference plus a penny whenever the basket would have been cheaper at a major rival.
From today (Thursday), if the Asda basket is not at least 10% cheaper than other major rivals, customers will receive a voucher that makes up the difference.
The pricing will be policed by mysupermarket.co.uk rather than Asda.
Andy Clarke, chief executive of Asda, said: "From today our price promise is backed by a copper-bottomed guarantee – if the basket of food you buy in our stores is not at least 10% cheaper than each of our major rivals, we'll put our hand in our pocket and give you back the difference.
"The Asda Price Guarantee cuts through all the phoney claims and headline numbers, and shows when it comes to saving people money, we mean business this year."
VAT-rated goods, around half of Asda's offering, will also be covered by the scheme.
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Asda's scheme could shore up customer loyalty after recent research showed that .
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