Sainsbury's and Asda have vowed to pass on £1 billion worth of price cuts to customers if its merger is allowed to go ahead.
Last month, the Competition and Markets Authority (CMA) raised concerns over the merger, saying it would likely reduce choice for customers and increase prices. It also said the supermarkets were not likely to be able to address its concerns.
Sainsbury's and Asda have stressed that the size of the combined company will allow £1.6bn worth of savings, and therefore pass on savings to customers at the tills. The pair have now said they will invite an independent body to verify its claims.
Sainsbury's has also said it will place a cap on the profits it can make through petrol sales to 3.5p per litre.
In a joint statement, Sainsbury's and Asda said the CMA's report contained "significant errors". They claim the CMA's threshold for concerns were at an "unprecedentedly low level", meaning a number of areas of concern were inevitable.
Of the £1bn price savings, the supermarkets said £300m would be invested within the first year of the merger taking place, and the remaining £700m over the following two years. Overall, it would bring prices down by an average of 10%.
In addition, Sainsbury's said it will pay small suppliers with less than £250,000 revenues within 14 days, while Asda will maintain its pledge to do the same.