The first minister has urged people to stay in this weekend as she revealed that eight more people with coronavirus had died in Scotland.
Nicola Sturgeon said the total number of deaths now stood at 33.
There have been 1,059 confirmed Covid-19 cases in Scotland - an increase of 165 since Thursday.
Chief medical officer Dr Catherine Calderwood said the actual number of people infected in Scotland could be more than 65,000.
Her previous estimate was that between 40,000 and 50,000 people were infected.
"There will come a time where I will be able to talk to you about the numbers being infected and that rate slowing," she told a media briefing in Edinburgh.
"But that time is not yet, and that time will not be for some weeks to come."
Ms Sturgeon said there were now 72 patients in intensive care units across Scotland.
As the country prepared to spend its first weekend in "lockdown", the first minister urged people to heed the "stay at home" message.
"The single most important thing anyone can do to show our support for the NHS is by staying at home," she said.
Ms Sturgeon acknowledged that the restrictions were "tough", especially for households with young people.
She urged them to "stick to the rules" - but added that they should "also remember to have fun".
"I appeal to young people, make sure you pick up the phone to your grandparents at the weekend, or Facetime to tell them how you're getting on, but also to check in on them and see how they're doing," she said.
"Staying at home, more than any other single measure, is the way you can protect and support our NHS."
Ms Sturgeon praised health workers as well as police who have been given new emergency powers to enforce the restrictions.
She said: "My fervent hope and belief is that the police will not have to enforce these rules very often."
Scotland's chief medical officer had another grim message for the public today. Up to 65,000 people in Scotland could already have coronavirus - and what's more, these are early days.
Dr Catherine Calderwood says Scotland is only beginning to see that steep acceleration of cases. That sadly will mean many more deaths, and acute pressure on our intensive care beds.
It's hoped that by introducing strict measures in Scotland now, it might stretch out demand on our most critical services, but that is a hope and nothing is certain.
Increasingly, we are hearing about frontline NHS staff becoming ill themselves.
Everyone needs to brace themselves for what is to come. The chief medical officer says it will be weeks before the tide will turn.
The first minister also announced £3.8m extra funding for NHS mental health support services, and said people should look at the NHS inform website for details of helplines and services.
Some of the money will be used to expand the mental health hub so that support can be given 24-hours-a-day to people who have called the NHS 24 helpline.
Ms Sturgeon also sent her "best wishes" to Prime Minister Boris Johnson after it emerged he had tested positive for Covid-19,.
The first minister said she had not been tested, and added: "I don't underestimate how difficult it is to be positive for this virus."
Dr Calderwood revealed that she and her counterparts elsewhere in the UK had agreed a protocol for testing "significant" figures.
These people would be tested only if there were clinical reasons in the first instance, said the chief medical officer.
However, there would be also tests for "significant people the loss of whom from government would make a big difference to our coronavirus effort," she said.