Ms Hart said that Wales would be happy to act alone in introducing minimum pricing if other UK countries did not make progress on the issue.
‘I am very clear that if we do not see the action we want at UK level very soon, then the time will come when we seek more powers to act ourselves,' she said.
Evidence suggests that after 10 years, a minimum unit price of between 40p and 50p could reduce the number of alcohol-related deaths in Wales by 20-25%, she said. ‘This would equate to 200-250 fewer deaths per year after 10 years.'
She added: ‘Some argue that a minimum price penalises all drinkers, not just those who drink to excess. I do not accept this argument - the impact on those who drink within sensible guidelines will be small. It is those who drink a lot more who will notice the difference, and therefore hopefully moderate the amount they consume, particularly young people.'
The BMA backed minimum pricing on alcohol in its pre-election manifesto.