Sainsbury’s and Asda have said they would sell between 125 and 150 supermarkets and a number of convenience stores if allowed to merge.
The supermarket giants would also sell some petrol stations, and Sainsbury’s has already said it would cap fuel profits for five years.
Earlier this week, the supermarkets also vowed £1bn in price cuts.
The CMA said last month it could block the merger between Sainsbury’s and Walmart-owned Asda.
In documents published by the CMA on Friday, the supermarkets claimed that shoppers would be deprived of lower prices should the £12bn deal be blocked.
The supermarkets described the Competition and Markets Authority’s (CMA) provisional findings into the merger, which warned the deal could be blocked unless they sold off significant stores or even one of the brands, as “prohibition in all but name”.
Their submission said that the CMA’s remedy proposal was “impossible to implement”.
They said they “categorically reject the CMA’s view that coming together will lead to a worse outcome for customers”.
Sainsbury’s boss Mike Coupe and Asda chief executive Roger Burnley said: “We have asked the CMA to correct significant errors in its provisional findings.
“Its analysis fundamentally misunderstands how people shop today as well as ignores the intensity of competition and the dynamism of the UK grocery market, which evolves on an almost weekly basis.”
The chief executives added: “We regret the uncertainty this process causes for our colleagues and want to reassure them that no stores would close because of this merger, with any divested stores run by a credible third party.”
The CMA’s final report is expected by 30 April.