The first cases of the new variant were reported in Scotland on Monday, with four in Lanarkshire and two in Greater Glasgow and Clyde.
Not all cases were linked to international travel, suggesting community transmission has begun. Five cases have so far been found in England, bringing the UK total to 11.
Nicola Sturgeon urged Scots not to panic, but did not rule out further domestic restrictions or a possible impact on Christmas.
In a joint letter with Welsh First Minister Mark Drakeford, Ms Sturgeon urged Boris Johnson to convene an urgent Cobra meeting and tighten rules around international travel, with all arrivals asked to self-isolate for eight days and take two PCR tests.
Both requests were denied by the Prime Minister, whose spokesperson said further restrictions would negatively impact the travel industry.
From 4am on Tuesday, passengers arriving to the UK will be required to take a PCR test on day two, and self-isolate until they receive a negative test. Ten southern African nations have been added to a four-nation travel red list.
Little is known about the new variant, but Ms Sturgeon said the Scottish Government will act with caution while there are still concerns it may be more transmissible than Delta, or respond differently to vaccines.
“What we do know at this stage confirms in my view that we should treat it seriously and that we should continue to act on a precautionary basis at this stage,” she told a media briefing on Monday.
“While we all hope that the emerging understanding of it will reduce rather than increase our level of concern, there is no doubt that this presents potentially the most challenging development in the course of the pandemic for quite some time.”
The Joint Committee on Vaccination and Immunisation (JCVI) issued new advice on Monday that all adults should be offered a booster vaccine dose, in a bid to increase protection before any potential wave of the Omicron variant.
Adults aged 18 to 39 will be offered a jag in descending age order, with priority also given to more vulnerable individuals. Those aged 40 and over are already eligible.
The committee has also reduced the waiting time recommended between second and third doses to three months.
The JCVI also advised young people aged 12 to 15 should be offered a second dose, no sooner than 12 weeks after their first dose.
All new advice will also apply to pregnant women, the JCVI said.
The Scottish Government said it was already working on extending the rollout.
“We welcome the further advice from the JCVI on the Covid-19 vaccination programme and confirm Scotland has already started work on its implementation, including the recommendation that boosters can now be given to all adults no less than three months after a second dose,” chief medical officer Dr Gregor Smith said.
“Urgent talks with health boards and vaccination partners are underway and further information on the delivery of this advice will follow as soon as possible.”
In a briefing on the JCVI decision, deputy chief medical officer of England Professor Jonathan Van-Tam urged people not to panic, but not to ignore the “weather forecast” coming from South Africa.
The number of mutations present in the Omicron variant “makes us worry about a possible effect on vaccine effectiveness”, he said.
But he added: “I do not want people to panic at this stage.
“If vaccine effectiveness is reduced – as seems pretty likely, to some extent – the biggest effects are likely to be in preventing infections and, hopefully, there will be smaller effects in preventing severe disease.”
Prof Van-Tam said vaccine boosting was the easiest thing to do while waiting for scientists to gather more information about Omicron.
Both Moderna and Pfizer vaccines can be given as a booster for adults, the JCVI said.
Those who are severely immunocompromised will be offered a fourth dose, having already been given three primary doses.
Professor Wei Shen Lim, chair of the JCVI, said: “Having a booster dose of the vaccine will help to increase our level of protection against the Omicron variant.
“This is an important way for us to reduce the impact of this variant on our lives, especially in the coming months.
“If you are eligible for a booster, please take up the offer and keep yourself protected as we head into winter.”
Ms Sturgeon asked the public to increase adherence to current anti-Covid measures in a bid to reduce spread of the Omicron variant, including testing regularly, wearing face coverings and working from home.
She said she “fervently hopes” the variant will not impact Christmas plans, but did not rule out a return to harsh restrictions.
“I'm not asking anybody today to put plans on hold,” she said.
“I will during this next phase of the pandemic if this proves necessary."
She added: “Standing here right now I still hope, really fervently hope, to be having a normal Christmas with my family. Can I say that in a 100 per cent sense? No, but that’s what I hope and I think that’s what we should be all be hopeful of as we learn more about this variant.”
Professor Jim Naismith, director of the Rosalind Franklin Institute at Oxford University, said it was likely the Omicron variant had a “foothold” in Scotland.
“The discovery of six cases in Scotland, some with no travel to South Africa or other ‘red’ list countries, is to be expected,” he said.
“Travel is in reality all or nothing with respect to Covid-19 variants. Rapidly spreading variants will move faster than surveillance systems.
“Stopping travel to one country, whilst allowing it from others has not been particularly effective because the virus is able to take multiple transit routes.
“Similarly discriminating between who is allowed to travel into a country on citizenship grounds has not worked well, since the virus is not interested in passports.
“Local zoning in the UK failed for the same reason and has little scientific basis. It seems likely the Omicron variant of the virus has a foothold here.”
Adam Finn, a professor of paediatrics at Bristol University and member of the JCVI, said higher levels of vaccination may be able to partly compensate for reduced efficacy, and that an increased rollout would only be useful if started before a wave of Omicron took hold.
“Both delivery of vaccines and generation of immune responses once administered take time,” he said.
"While it is better to wait for plenty of solid evidence to drive policy whenever you can, we currently face a situation where doing that could substantially increase additional risk and could render any actions ineffective through delay.”