A further 13 people with coronavirus have died in Scotland, bringing the total to 60.
First Minister Nicola Sturgeon said a total of 1,993 people had now tested positive for the virus, up from 1,563 on Monday.
However, 108 of these were from a laboratory which had been unable to submit data over the weekend.
Ms Sturgeon said this partially explained the big increase in the number of positive tests.
But she stressed that the actual number of cases of Covid-19 in Scotland is likely to be far higher than the figures show.
There are currently 135 patients with the virus in hospital intensive care units - an increase of 27 from Monday.
Ms Sturgeon also said that about 6% of NHS staff in Scotland were currently off work because they had coronavirus symptoms or were self-isolating.
She said this figure was "relatively low" and was expected to increase, but said testing of key workers was now being rolled out and would help "get people back to work as quickly as possible".
With the UK-wide lockdown now in its second week, Ms Sturgeon urged people to continue to stick to the social distancing rules, adding: "By following this advice you are helping us save lives."
The number of deaths announced by the government each day is currently based on those who have died in hospital after having laboratory-confirmed cases of coronavirus.
The figure will soon also include those who died outside of hospital and who were "presumed" by a doctor to have had the virus, even if they were not tested.
Scotland's chief medical officer, Catherine Calderwood, said it was unlikely there had been a "significant" underestimate in the number of deaths so far.
This is because there are not widespread examples of people becoming very unwell without going to hospital.
Ms Calderwood said the proportion of tests that were giving positive results for coronavirus was "increasing day by day".
She said the only group that was not seeing a sustained increase in the number of confirmed cases was those under the age of 15, which she said was in line with the experience of other countries across the world.
She added: "Despite what we are doing, the virus is still being transmitted in our communities".
The daily Scottish government briefing was held as emergency powers to help tackle the coronavirus crisis were unveiled at the Scottish Parliament.
The Coronavirus (Scotland) Bill, which will be debated by MSPs on Wednesday, covers a wide variety of areas including special measures for court trials which would normally go before a jury, and safeguarding tenants from eviction.
The provisions in the bill will expire on 30 September unless the Scottish Parliament approves an extension for a further six months.
Ms Sturgeon said the legislation was "an unprecedented response to an unprecedented situation", saying powers "will not remain in force any longer than is absolutely necessary".