The Health Secretary still "firmly" believes that minimum pricing meets European law.
Alex Neil also insisted that the measure is the "most effective and efficient way to tackle alcohol misuse in Scotland".
He spoke out after it emerged that Europe has raised concerns about the Scottish Government's plans for a minimum price.
The European Commission (EC) has joined five European Union nations in submitting legal questions about the controversial legislation, passed by Holyrood in April.
The Scottish Government wants to set a floor price of 50p per unit in an attempt to tackle the nation's unhealthy relationship with alcohol.
Critics have raised concerns that it may fall foul of European trade rules but ministers argue that the policy is justified on public health grounds. A spokesman at the EC's Industry and Entrepreneurship Directorate said last week that while it "fully shared" the aim of the legislation to tackle alcohol abuse, there was a "technical objection".
Mr Neil told MSPs on Tuesday that the Scottish Government has until December 27 to respond to the issues raised in the EC's opinion on minimum pricing.
While the issues raised by the EC in the opinion are confidential, he said: "We're confident we can demonstrate minimum pricing is justified on the basis of public health and social grounds, and we will continue to press the case for minimum pricing in the strongest possible terms."
Mr Neil was questioned on the legality of minimum pricing at Holyrood. He responded: "We've always been clear in order to be compliant with EU law we need to demonstrate that minimum pricing is justified under public health grounds and it is the most proportionate means by which to deliver our public health objectives.
"I firmly believe that Scotland's record of alcohol-related harm means that the introduction of minimum unit pricing is fully justified on public health grounds. Furthermore, I am clear that minimum unit pricing is the least intrusive mechanism through which to reduce the disproportionate level of alcohol-related harm attributed to high-strength, low-cost alcoholic products.
"For these reasons the Scottish Government remains firmly of the view that minimum unit pricing complies with EU law. We remain firm in the belief a minimum price per unit of alcohol is the most effective and efficient way to tackle alcohol misuse in Scotland."
Last month it was revealed that Bulgaria raised an objection to the legislation. It has now been joined by France, Italy, Portugal and Spain. The Scotch Whisky Association lodged a complaint with the European Commission earlier in the summer and is pursuing action through the Court of Session in Scotland.