But restrictions on indoor events and hospitality will remain until at least January 24, sparking anger among hospitality leaders.
It comes as 10,392 new cases were recorded on Tuesday, while 1,479 people were in hospital and 54 in intensive care.
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Outdoor gatherings of more than 500 people will be permitted from Monday, meaning coming football and rugby matches, including Six Nations fixtures, can take place.
But the Covid certification scheme will be tightened, with events of more than 1,000 people required to check the status of at least half of attendees or at least 1,000 people, whichever is higher.
From Monday the requirement to be “fully vaccinated” for the certificate will be increased to three doses for those whose second dose was more than four months ago. A negative lateral flow test will remain a valid alternative.
And the Scottish Government is considering extending the scope of the certification scheme to other settings, Ms Sturgeon said.
The Scottish Liberal Democrats labelled this “concerning”.
“The prospect of rolling this out to a new array of venues, particularly when many of those venues are pulling themselves off the mat following the latest hospitality rules, is also highly concerning,” said party leader Alex Cole-Hamilton.
“A mere short five days’ notice for extra measures concerning large events is not sufficient to provide enough logistical planning for businesses and events. There have been warnings before that bottlenecks in crowds are a safety risk and could lead to transmission.”
Scottish Conservative leader Douglas Ross said it was “disappointing” the Government was re-visiting the possible extension to Covid certification.
“The Government cannot even prove that this scheme reduces the spread of the virus,” he said.
“This move will have damaging consequences across our economy.”
Indoor events will continue to be limited to 200 people seated or 100 people standing, and requiring table service in hospitality settings, until at least January 24, pending a review of data by ministers.
The advice to the public to limit contact with other households as much as possible will also remain.
The Scottish Chambers of Commerce called for extra funding for businesses required to check more certificates to compensate for the staff and resources needed.
Retail and hospitality businesses will find it “incredibly disappointing” that indoor restrictions have not yet been lifted, said chief executive Dr Liz Cameron.
Dr Leon Thompson, director of UKHospitality Scotland, said these continued measures have “torpedoed” businesses hopes.
"The First Minister talked about a gradual easing of restrictions, but our sector has been closed or restricted for almost two years now,” he said.
"Any positivity that could be taken from possible changes on the near horizon was scuppered with further talk of vaccine passports and possible wider application.
"The phrase ‘living with Covid’ sounds more and more like ‘living with significant ongoing restrictions’.”
The Scottish Licensed Trade Association (SLTA) accused the Government of leaving licensed traders in “limbo” waiting for January 24.
“If the passport scheme is extended to hospitality settings, it will have a major negative impact on businesses,” said SLTA managing director Colin Wilkinson.
The Night Time Industries Association Scotland, which represents nightclubs, said it was disappointing venues would not be allowed to reopen until at least January 24.
A spokesperson said suggestions of an extension to the Covid certification scheme were “very worrying”.
The Federation of Small Businesses said local and independent businesses would welcome the easing of some restrictions by Ms Sturgeon, and look forward to further curbs being lifted.
“Businesses will accept trade-offs as we return to more normal trading conditions,” said Scotland policy chair Andrew McRae. “But ministers should remember that Covid rules place a disproportionate burden on small operators, especially as they consider the role of vaccine passports.”
The measures which continue in hospitality settings make profitability impossible for thousands of community pubs and independent breweries, the society of independent brewers added.
Scotland has begun to “turn a corner" in its pandemic response, the First Minister told MSPs, and the Government is working on an adapted framework for “living with” the virus to be published in coming weeks.
This will involve considering what adaptations can be made to life to make things safer for everyone, Ms Sturgeon said.
"Because of the efforts we have all made, we are in a better position than I feared would be the case when additional measures were announced in December,” she said.
"And I hope we are now seeing signs of improvement. That is allowing us to start the process from Monday of lifting the additional restrictions – and I hope that next week I will be able to confirm further steps in that process.”
Mr Cole-Hamilton raised concerns this new strategy may increase the number of Scots living with long Covid, and called on the Government to better support sufferers.
“The First Minister talks about living with the virus,” he said. “That’s a concept all too familiar for the 100,000 Scots living with long Covid and that number is surely going to rise with the surge we are currently facing.
“More than 100 days have passed since the Government published its meagre long Covid action plan and sufferers still haven’t seen any difference.
“Where are the long Covid clinics, the care pathways and the long Covid nurses that sufferers have called for? People living with long Covid need immediate help and support.”
Health secretary Humza Yousaf said “living with Covid” would not mean abandoning vulnerable people.
"We’re going to have some element of protective measures such as, for example, I suspect wearing face coverings in certain circumstances for a while yet to come,” he said.
“Those basic mitigations are going to be important even when Covid goes from pandemic to endemic.”
Asked about the concerns of vulnerable people and carers, Mr Yousaf said: “I give them a reassurance that when we talk about living with Covid, we’re not talking about simply abandoning everything, simply throwing caution to the wind.”
Scottish Labour’s Anas Sarwar welcomed the idea of a new framework for dealing with Covid, but called for “clear trigger points” for bringing in any further restrictions in future.
“A new phase of the pandemic must mean a new approach – one that recognises we will be living with Covid in some form for years to come,” he said.
“This means building resilience back into the heart of the NHS, but also into our economy, and recognising the toll the past two years has taken on the mental health of so many Scots.
“People cannot live their lives waiting for ad-hoc updates on what the rules will be day-to-day.”
Mr Ross said: “The First Minister says we need to learn to live with Covid. But, after more than two years, people across Scotland have already learned to live with Covid.
“By now, people understand what’s necessary to combat this virus. We have to trust their judgement more as we move forward.
“We should now be looking to get a balance that is much more in favour of our economy and wider public health concerns around physical and mental health.”