Morrison's, the country's fourth largest supermarket, has added its support to Tesco's call for minimum pricing.
But it has told the government it wants to achieve this via duty and VAT rather than setting unit prices on drinks.
It has written to Theresa May, the home secretary, to say it supports the efforts to "tackle the misuse of alcohol" in society.
However, it warned that current plans to ban below-cost selling would be difficult to implement as retailers pay different amounts for alcohol depending on the deals they cut with suppliers.
The supermarket said it wants to ban the sale of alcohol below a set rate of duty — and value-added tax determined by the government.
Under Morrison's proposals the government would not set a minimum unit price on alcoholic drinks but would instead set a base price linked to the rate of duty and VAT.
"This enables a floor price without the government intervening in the market," said Richard Taylor, director of corporate affairs at Morrison's.
"It also means that additional revenue from raising prices on alcohol would go to the exchequer rather than the retailer. The proposal aims to ensure a level playing field for retailers."
The National Institute for Health and Clinical Excellence (NICE) supports minimum unit pricing as does the Scottish government, which is trying to pass legislation to this effect.
NICE estimates that the annual cost of alcohol addiction to the National Health Service is £2.7bn.