The First Minister stopped short of replicating a pledge by Boris Johnson for England to vaccinate everyone in four key priority groups by mid-February, citing a lack of clarity about vaccine supplies.
But Ms Sturgeon said health officials in Scotland would "bust a gut" to ensure all care home residents, their carers, everyone over the age of 70, all frontline health and social care workers and everyone who is clinically extremely vulnerable get the jab by the middle of next month in line with the pledge south of the Border.
"At the moment the biggest unknown that stops me being able to answer the question about how much sooner would I like to be able to do it is I don't know, beyond the end of January with enough certainty, what the flow of supplies is going to be," Ms Sturgeon said at Tuesday’s coronavirus briefing.
"The commitment the Prime Minister gave last night, I don't yet have enough certainty on supply beyond the end of January to say categorically looking down the camera that we think we can do those first groups of the priority list by mid-February, as the Prime Minister said.
"Do I want to do that? Yes. If we get supplies that allow that, will we bust every gut and move every mountain to deliver that? Yes, we absolutely will.
"But for me to say with certainty right now that we can do that before having the certainty of the supply would be putting the cart before the horse."
More than 100,000 Scots have already been vaccinated with the Pfizer/BioNTech jab, but the arrival of the UK's Oxford/AstraZeneca vaccine, which is far easier to manage, is expected to ramp up inoculation levels.
There have been 2,300 vaccinators recruited in Scotland to distribute the jab.
Ms Sturgeon has already said she plans to roll out the vaccine to all under-50s and people below this age with health conditions by early May. This would cover about half the Scottish population.
The SNP leader said she was wary of "undermining" public confidence by making commitments which ministers would subsequently unable to deliver on.
"That's how we're going to try and do this, but underlying all of that is a determination I want to get vaccines into peoples' arms as quickly as possible," Ms Sturgeon said.
"I want that as much as anybody else does and we're giving this the greatest priority and focus that we possible can and to get it done as quickly as possible."
National clinical director Professor Jason Leitch said that an extensive network of facilities would be utilised to deliver the vaccine.
"The number of vaccination centres is thousands," he said of the plans for Scotland.
“We will use every GP’s surgery because that's a simple network that we will have access to and then we will have a very small number of big vaccination centres."