The First Minister said the absence of new fatalities was "really significant" as it was the first time this has happened during the week. Previous instances of zero deaths have occurred at weekends when reporting rates tend to be lower.
"Suppressing the virus, trying to get as far as we can towards total elimination has to be our overriding priority," she said at her Daily Coronavirus briefing today.
"We're made exceptional progress today over the past three months and the figures today highlight that.
"But it has only been possible because the vast majority have stuck to the rules."
The latest figures today also show 17 new positive cases - with just 0.3% of tests in Scotland now producing a positive result. The number of hospital and intensive care cases are also down to 823 and 17 respectively. Deaths for those who have tested positive remains unchanged at 2,482.
Total elimination will not mean that the virus disappears completely in the community, but that cases become so sporadic and isolated that it will become more straightfoward to the authorities to control.
Ms Sturgeon explained: "It doesn't mean it has gone away, it doesn't mean it will stop rising again if we stop doing the things we need to do. It gives us more confidence that we can keep it under control with surveillance and testing, contact tracing and where we see outbreaks using very targeted measures as opposed to blanket lockdowns.
"How far away are we from that? I think we are not that far away that - the challenge is keeping it there."
This involves persisting with social distancing and hygiene measures.
"It also means we have to be very vigilant with people coming into Scotland from other parts of the world or even other parts of the UK where infection rates might be higher," the First Minister said.
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