Retailers say heavy drinking is partly a cultural problem
Setting a minimum price for alcohol would be a "blunt instrument" which would not tackle binge drinking, supermarket chiefs have told MPs.
The Commons Health Select Committee, which is investigating alcohol abuse, was told that fixing alcohol prices would not be a "silver bullet".
Scotland is considering minimum prices but the UK government is sceptical.
Sainsbury's executive Nick Grant said there should be a crackdown on drunk customers still being served.
Existing laws designed to stop intoxicated people from buying more alcohol were not being properly enforced, he told MPs, adding this would "save lives and police time".
Many MPs on the committee said they believed that minimum pricing should be considered as one way of curbing heavy drinking, which was putting a huge strain on the NHS.
Labour MP Doug Naysmith said alcohol promotions in supermarkets were "contributing" to the problem.
Alternative strategies, such as labels on bottles and advertising campaigns warning about the dangers of excessive consumption of alcohol, had clearly not worked.
"You say you want to improve this but nothing much is happening," he told representatives of Sainsbury's, Asda and Waitrose.
But Asda executive Paul Kelly said minimum prices would be a "stealth tax" which would hit those on low and fixed incomes without tackling the root causes of excessive drinking.
"Minimum price is not the silver bullet that it has often been made out to be," he said.
He questioned the effectiveness of minimum pricing, saying heavy drinkers would compensate for having to pay more for alcohol by "simply looking to spend less in other areas".
It would also mean "taxing responsible, hard-working families" who were moderate drinkers would be hit.
He acknowledged that messages about responsible drinking could be more consistent and lessons could be learnt from anti-obesity campaigns about how to change attitudes to consumption.
Labour MP Kevin Barron, who chairs the committee, said he could not enter a supermarket in his constituency without "tripping over" drinks promotions such as "three for two" offers.
But Mr Grant said alcohol promotions were popular with customers and were a "product of a fiercely competitive market" in which different retailers were fighting for business.
He said education, not price, was the best way to change consumer behaviour, saying France should be the model for a more "relaxed and sensible" approach to alcohol.
In March the chief medical officer for England and Wales, Sir Liam Donaldson, proposed a minimum price of 50 pence per unit of alcohol, which would effectively double the cost of some drinks.
Ministers said they would study his report while indicating they did not favour measures which would punish moderate drinkers.
Scottish ministers are considering minimum pricing to try to force a "culture change" but no price has been decided.
At the hearing, the supermarkets also rejected suggestions that their cheap promotions were directly contributing to pub closures.
"Their cost of business is higher, smoking has had a big impact, I think the drift away from town centres, the strength of Saturday night television - there are a whole series of factors," Mr Kelly said.