But health secretary Nicola Sturgeon still favours such a move and has offered an option for a trial period followed by a vote to remove it if MSPs think it isn’t effective.
The offer was made at a cross-party summit on the issue yesterday, at which opposition parties urged the ruling SNP to fall in line with Westminster on a proposed ban on selling below duty and VAT.
Speaking after the meeting, Sturgeon said: "We agreed that action on price was an essential part of tackling Scotland's alcohol misuse problems.
"We will consider any workable alternatives, and as a result have asked the opposition parties to submit further details on what they have proposed today.
"In an attempt to reach agreement, I indicated that the government would be willing to introduce a sunset clause to the minimum price section of the Alcohol Bill currently going through the Scottish Parliament.
"This would have the effect of ensuring that the minimum price policy is reviewed after a set period.
“If minimum pricing proved to be successful the measure would be retained, if not parliament could choose to end minimum pricing.
"Such a measure would allow minimum pricing to be tested and evaluated over time, and I hope would address some of the concerns colleagues have expressed."