It is a year since the policy - which sets a floor price of 50p a unit - was due to be brought in across Scotland.
Despite widespread support among health professionals and police, it was immediately tied up in a legal challenge led by the Scotch Whisky Association (SWA) which argues it is illegal, will damage the industry and will not target hazardous drinkers.
A joint letter from figures in the British Medical Association (BMA) and a former chief medical officer for Scotland now calls on the SWA to drop its opposition.
"The SWA has mirrored the tactics of the tobacco industry in delaying life-saving legislation," according to the letter.
"It opposes any measure that might affect its profits, no matter the obvious benefits to people's health.
"By taking this legal action, it is undermining the united view of the Scottish Parliament and costing taxpayers thousands of pounds in legal bills."
Adopting the policy is a crucial first step in addressing Scotland's problem with drink, the group argues.
"Minimum pricing will cut alcohol-related hospital admissions and save lives. We cannot afford to delay any longer," the letter adds.
The 22 signatories include Dr Evelyn Gillan, chief executive of Alcohol Focus Scotland, Dr Brian Keighley, chairman of the BMA in Scotland, and former chief medical officer Dr Mac Armstrong.
Dr Gillan said: "In Canada, a 10% increase in average minimum alcohol prices was associated with a 32% reduction in alcohol deaths. We appeal to the SWA to drop their legal challenge and let Scots benefit from this important health policy."
Dr Richard Watson, a GP in Glasgow who supports the pricing policy, said he sees alcohol-related harm every working hour.
"We've got a 24-year-old girl who has advanced alcoholic liver disease and is almost certain to die shortly," he said.
"When I was a medical student 30 years ago, nobody had alcoholic liver disease until they were in their 40s. But she's been drinking five or six litres of strong white cider daily since her early teens.
"This is the cheapest way of buying alcohol - it can cost as little as 18p per unit. Strong white cider is the sort of alcohol that will be seriously affected by minimum pricing. It's simply inconceivable that she would be able to buy six litres of cider a day if it cost 50p a unit."
David Frost, chief executive of the SWA, said: "We are committed to tackling alcohol misuse through legal and effective measures, for example through our new Scotch Whisky Action Fund. However, we believe that minimum unit pricing is illegal, wouldn't target harmful and hazardous drinkers and would damage the Scotch whisky industry.
"Minimum unit pricing is based on modelling, not concrete evidence. The right way forward is targeted help where there are problems, not blanket policies which penalise the vast majority of responsible drinkers. With alcohol-related deaths and harms falling in Scotland, we should build on measures in place which seem to be working.
"The SWA has consistently called for the legal case to be fast-tracked to the European Court of Justice so that we can speed up the process, but the Scottish Government refused to agree to this move. I regret that the debate on alcohol policy has become so polarised. We would like to work to build a broader and better consensus."