The Scottish government has pledged to consider "any workable alternatives" to a minimum price for a unit of alcohol.
The move came after an all-party meeting at Holyrood aimed at tackling Scotland's drink problem.
The health secretary told the meeting she would be willing to introduce a "sunset clause" allowing parliament to scrap the policy if it was not working.
Opposition parties issued a statement urging ministers to work with the UK government to impose a floor price.
The parties said this would build on the combined cost of duty and VAT.
Speaking after Wednesday afternoon's meeting, Ms Sturgeon said there had been agreement that action on price was an "essential part" of tackling alcohol misuse.
She said: "The Scottish government has proposed minimum pricing as the most effective way of doing this.
"However, following today's meeting 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."
The meeting was proposed by opposition parties in a bid to find common ground on the issue of problem drinking, and was attended by members of all five Holyrood parties.
Afterwards, Labour's Jackie Baillie said: "We all agree that raising the price of alcohol has a part to play in reducing consumption and therefore harm and we are putting forward a better alternative to minimum unit pricing.
"I want to see the Scottish government working together with the UK government to impose a floor price on alcohol that would prevent retailers from selling drink at irresponsibly low prices."
Ms Sturgeon had said before the meeting that she would confirm the proposed minimum price for a unit of alcohol before the next stage of the Alcohol (Scotland) Bill.