Tesco's new lines will sit in a price range above its existing Value range, but well below big-name brands in each category. For example, its 160-pack of Packers Best teabags will cost £1.69 compared with £3.18 for PG Tips.
Tesco is reserving separate aisles for the 350 new products and also launching a TV and press campaign today to support them, in addition to using Clubcard data to communicate the change to shoppers it believes to have been lured by rivals.
Asda's focus is on cutting the price of every product in its value range, Smart Price, and of well-known frequently purchased brands - in all 5,000 products.
Andy Bond, chief executive of Asda, said that despite yesterday's record official figure of 14.5% for food price inflation, he is confident food prices have peaked and wants to help customers.
"That's why I'm determined that, as and when cost prices fall, it will be Asda which leads the charge and drives down prices for shoppers not just in the short term but permanently," he said.
The latest battle in the price war coincides with the release of 12-week grocery market figures from TNS Worldpanel, which show the 7.3% increase in turnover year-on-year is almost entirely due to food price inflation and not volume growth.
Tesco's market share has fallen from 31.7% to 31.5% while Asda's has climbed from 17% to 17.3%. Sainsbury's is down from 16% to 15.8% and Morrisons is up from 10.8% to 11%.
Discounters Aldi and Lidl are both up; Aldi from 2.6% to 2.9% and Lidl from 2.3% to 2.4%.