Nicola Sturgeon said winter will be "challenging" as coronavirus infections remain high and hospitals face intense pressure.
The admission follows alarm from front-line health staff about the impact of Covid in hospitals.
Scotland is covered by a patchwork of area restrictions to stem the spread of Covid-19, and Sturgeon is still prepared to put the whole country in tighter lockdown. But the Scottish Government leader has also claimed "encouraging" signs in recent days.
At Holyrood, the First Minister insisted she listens carefully to experts, adding: "We are not short right now of beds or staff but we do face a very, very challenging winter.
"That is true of Scotland it is true of England, Wales, Northern Ireland and indeed much of Europe and the world.
"That is exactly why I am asking people to continue to exercise the utmost caution as we try to ensure cases of Covid do not rise and the rise does not accelerate."
Earlier this week, leading medic Jackie Taylor, president of the Royal College of Physicians and Surgeons of Glasgow, said the government needs a "coherent strategy" for testing staff and patients in hospitals.
"Speaking to colleagues across the central belt in particular and the health boards which have the highest number of cases, we really feel as though we are facing a perfect storm,” prof Taylor said in a BBC interview.
"We have a significant number of cases, we have a shortage of beds and we have significant staff shortages because of illness and staff isolating.
"Obviously winter is always busier, and we are facing those months now."
Today, Sturgeon said there is still positive news. Hospital admissions and the need for intensive care have improved on recent weeks. The "R number" which explains the rate of infection spread is "hovering around one", suggesting restrictions are working.
But Sturgeon also confirmed another 39 Covid deaths and 1216 positive tests in Scotland over the past 24 hours.
Scottish Conservative Holyrood leader Ruth Davidson raised prof Kay's comment at First Minister's Questions today, demanding action from the SNP Government to address concerns.
Davidson said: "Just days after the SNP Government published its Winter Preparedness Plan, senior medics have already warned that the plans are not good enough.
"Scotland's NHS is facing a potential shortage of beds and staff this winter, all while Covid-19 cases rise and waiting lists for crucial treatments keep growing longer."
The First Minister said: "I am, apart from those who work in our health service, probably the last person who would stand here and say anything other than our health service is under intense pressure."
Sturgeon said close attention to the details informs local lockdown decisions.
No part of Scotland is yet at the highest level four stage. But with the UK Government confirming an extension to furlough wage support, it could still be imposed.
"England is in full lockdown - I can't rule that out for all or part of Scotland but as of now we are in a better position," Sturgeon said.
