It is the first time since mid-February that more than 1,000 daily cases have been reported.
A total of 242,875 people have now tested positive for the virus since the start of the pandemic.
The death toll under this daily measure – of people who first tested positive for the virus within the previous 28 days – now stands at at 7,678.
The daily test positivity rate is 3 per cent, down from 5 per cent the previous day.
A total of 121 people were in hospital on Tuesday with recently confirmed Covid-19, no change on the previous day, with 14 patients in intensive care, up two.
So far, 3,422,431 people have received the first dose of a Covid-19 vaccination and 2,313,695 have received their second dose.
It comes as new National Records of Scotland (NRS) figures show a total of 10,130 people have died in Scotland with confirmed or suspected coronavirus.
Latest data shows that eight fatalities that mentioned Covid-19 on the death certificate were registered in the week to June 6, the same as the previous week.
One was under 65, two were in the 65-74 age group and five were aged 75 or over.
There were three deaths in South Ayrshire and two in Glasgow City and North Lanarkshire. The Scottish Borders recorded one death.
The statistics are published weekly and cover all deaths registered in Scotland where Covid-19 was mentioned on the death certificate.