The Tesco Price Promise is a money-back pledge that compares the price of goods in a shopper's trolley at the checkout with prices at rival supermarkets Asda, Sainsbury's and Morrisons.
Any difference on comparable products is then refunded in the form of a Tesco voucher worth up to £10.
Sainsbury's believes the pledge misleads consumers because it does not make fair comparisons by, for example, matching products such as its Everyday Value Tea, which is not Fairtrade, with Sainsbury's basics tea, which is.
It added the pledge is also misleading on its basics water, which comes from a spring in Yorkshire, and is compared with Tesco's Everyday Value water, which Sainsbury's claims starts at the mains supply.
Sainsbury's is stepping up its fight against Tesco's Price Promise campaign in a long-running row over comparisons between the two firm's products.
Britain's third-biggest supermarket chain is to take its battle into the courtroom, by requesting a judicial review against a ruling by the Advertising Standards Authority (ASA) that rejected its complaint over the Tesco pledge.
The move comes after Sainsbury's lost an appeal against the ASA decision earlier this month, when a report by the watchdog's independent reviewer Sir Hayden Philips backed the ASA findings.
Mike Coupe, Sainsbury's commercial director, said it was "time to take a stand" on behalf of customers to ensure shopping decisions are not just based on price, but also factors such as ethics and provenance.
Supermarkets that are committing to reduce levels of saturated fat in their products is a "step in the right direction", but it was "no where near enough", the spokesman for the National Obesity Forum warned today.
Tam Fry, who is also the chairman of the Child Growth Foundation, told ITV News that the industry "does not want the regulations".
Societies that consume more products with animal fat tend to have higher risks of heart disease, the consultant cardiologist at the London Chest Hospital told ITV News.
Dr Charles Knight recommended people to adopt a Mediterranean diet, which is "rich" in olive oil, fruits and nuts.
The government should consider “proper regulation” to tackle high levels of saturated fat, say campaigners.
Tam Fry, trustee of the National Obesity Forum, added: "This latest piece of hype from the Department of Health will still mean over 50% of food will still have extreme levels of saturated fat.
"The much vaunted voluntary Responsibility Deal will never succeed until the Government takes a grip and makes everybody sign up to it."
Labour public health spokeswoman Luciana Berger says the government’s attempts to reduce saturated fat in supermarket food has little chance of succeeding.
She said: "A few company names on a non-binding plan with no timescale stands little chance of delivering the fundamental change needed to improve our national diet.
"Labour has put forward bold ideas to set legal limits on our food's fat, sugar and salt content and achieve a cross-party ambition for a more physically-active nation."
Kit Kat chocolate bars will not taste any different despite a new recipe with less saturated fat, according to a spokesman for Nestle. The firm, which manufactures Kit Kats in York, has signed a government pledge to reduce the amount of saturated fat in the UK diet.
Michelle Roberts, the company's Head of Nutrition, said the firm has spent three years researching the new recipe.
Public Health Minister Jane Ellison has praised firms including Sainsbury's, Tesco, Morrisons and Nestle for committing to reduce saturated fat in products as part of a new ‘responsibility deal’.
One in six male deaths and one in nine female deaths are from coronary heart disease - this is why it's critical that we challenge the way we eat and that we all make changes where we can.
It's hugely encouraging that companies providing almost half of the food available on the UK market have committed to this new Responsibility Deal pledge and they are leading the way to give their customers healthier products and lower fat alternatives.