NICOLA Sturgeon said it was better to "err on the side of caution" on Covid testing even if it means generating more false positives.
It comes after Public Health England issued new guidance to laboratories south of the border asking them to set a threshold for the amount of viral material needed before a positive test would be considered accurate.
Positive results outwith this "limit of detection" should trigger repeat testing, said PHE, before contact tracing is initiated.
PHE said: "It is necessary to strike a balance between the risk of false positive test results and an acceptable level of delay in test turnaround time (time taken to report results)."
The new guidance, issued on Monday, followed concerns raised by scientists that the rise in the number of Covid cases across the UK is partly due to people testing positive when they are no longer infectious.
The PCR test used to detect Covid-19 picks up genetic material from the virus.
READ MORE: Why an apparent rise in Covid cases might not be what it seems
However, this can include live virus as well as 'dead' viral remnants, that are no longer replicating.
At low levels this can indicate someone who is pre-symptomatic but still contagious, and about to develop full-blown infection.
But a low level - or "weak positive" - result can also mean someone had the infection weeks earlier, has recovered, and no longer poses a danger.
Academics including Professor Carl Heneghan, of the Centre for Evidence-based Medicine (CEBM) at Oxford University, said that this could partly explain why a rise in cases of Covid in the UK was not being fully reflected in a corresponding increase in hospital admissions.
In Scotland there were 40 new admissions to hospital for Covid in the three weeks to August 31, with 1451 detected over the same period.
Prof Heneghan called for a cut-off point to be set for positive test results so that people were not contact traced or asked to quarantine unnecessarily.
He said this would give a truer picture of the scale of the pandemic.
Prof Heneghan said: “Evidence is mounting that a good proportion of ‘new’ mild cases and people re-testing positive after quarantine or discharge from hospital are not infectious, but are simply clearing harmless virus particles which their immune system has efficiently dealt with.”
He described the latest guidance from PHE as an "interesting development".
READ MORE: Top academic says Scotland may be 'overcounting' Covid patient numbers
In relation to positive tests from individuals in the community, PHE says results at the limits of detection should trigger a repeat test.
It adds: "Contact tracing should only be initiated if there is a positive result from the repeat sample.
"A positive result at the limit of detection from the repeat sample is suggestive of the late stage cycle of infection and therefore contact tracing and further self isolation is not advised."
Retesting of hospital 'Pillar 1' patients is also recommended, but PHE said a second 'weak positive' result "should be interpreted in the context of the clinical presentation".
However, the First Minister said there are currently no plans to issue similar guidance here.
"When it comes to contact tracing, I guess my view as a politician is that we should still err a bit on the side of caution, rather than the opposite, so that we're catching as many people as we possibly can," said Ms Sturgeon.
The lower the prevalence of the virus in the population, the higher the risk of false positives becomes.
At very low levels, false positives can actually outnumber genuine positives.
Professor Jason Leitch, Scotland's national clinical director, said it was widely known that the PCR test can only detect genetic material of the virus, but cannot distinguish between live or dead virus.
He said: "We can't tell [from a swab] if you're infectious when that test is positive.
"But we can't tell if you're not - and it's the best judge we've got.
"We now know people shed virus for about 48 hours before you show symptoms and for about a week afterwards. In that 10 day period, that's when they are infectious.
"We can't always know because the test might be nearer the end of that period or nearer the beginning, so we've got to err on the side of caution - both for that individual self-isolating, and their contacts."
Prof Leitch said as the science improves tests could be developed that "allow us to say yes, no, or maybe - and they're the ones you re-test".
He said it was currently up to clinicians to order a repeat test if they had concerns about a 'weak positive' result.
Data published yesterday shows that just under 132,000 tests have been carried out in the past week, but only 67,209 people were newly tested.
That suggests thousands have been repeat tests, although that will include staff and patients who are being regularly swabbed in hospitals and care homes, not necessarily people in the community.
Prof Leitch added: "Public Health England haven't said 're-test all the positives'.
"But in some laboratories you can go deeper in the machines to understand a bit more about what the virus is doing and showing.
"In the meantime, even though the test isn't strictly a yes-no test, we have to treat it as if it is because we have no choice."
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