Scotland has recorded a record-high 15,849 new coronavirus cases in the past 24 hours, Nicola Sturgeon confirmed but she has announced no new restrictions.

The number of new infections is 4,819 more than the previous high, which was recorded on Boxing Day.

The First Minister told a virtual meeting of the Scottish Parliament that the expected wave of Omicron infections is now rapidly developing, as she warned a further steep rise in cases is expected for the days and possibly weeks ahead.

She said the test positivity rate is 28.9%, with Omicron now accounting for around 80% of cases, with overall infections having risen by 47% in the past week.

Ms Sturgeon told MSPs: “Given the speed and extent of transmission now, it is vital that we continue to take sensible precautions and limit social interactions for a further period, as we learn more about the likely impact of this wave of infection and complete the booster programme.”

She said restrictions on hospitality, events and retail are expected to remain in place until January 17.

New rules on social gatherings came in on Monday, with meetings limited to three households at indoor and outdoor venues like bars, restaurants, theatres, cinemas and gyms.

A day earlier, restrictions were brought in to ensure one-metre physical distancing at large events, with limits of 100 people standing indoors, 200 people sitting indoors and 500 people outdoors.

Ms Sturgeon said: “Over Hogmanay and New Year’s Day, and for at least the first week in January, we are advising everyone to stay at home more than normal, to reduce contacts with people outside our own households, and to limit the size of any indoor social gatherings that do take place so that they don’t include people from any more than three households.”

She said she hopes to reach a decision on any shortening of the isolation period requirement for household contacts of cases “in the next week”, with any changes taking effect from January 5.

The First Minister also announced some PCR test appointments will be prioritised for essential workers, the clinically vulnerable and those eligible for new Covid-19 treatments, amid problems with accessing the tests.

She said: “I would expect that within the next couple of weeks, we will have a clearer picture and that this will then help us reach informed judgments about the most proportionate response going forward.

“In the meantime, however, while we better understand the impacts and while more and more of us get the added protection of booster vaccinations – which will help reduce the impacts – we must try to avoid the sheer volume of cases overwhelming us.

“That is why it is prudent, indeed essential, that we slow transmission as much as possible.”

Giving a further update on the daily figures, she said three more people had died after testing positive for the virus, taking the total number of coronavirus-related deaths to 9,836.

As of Tuesday night, 679 people were in hospital with Covid-19, 80 more than the previous day, and 36 were in intensive care – a decrease of one.

Ms Sturgeon also set out the allocation of £100 million of a £275 million business support fund, including £32 million for hospitality and leisure, with an additional £10 million for those hit most by table-service only being allowed in venues which serve alcohol.

Up to £5 million is going to shuttered nightclubs, £27 million to the culture sector and £17 million to events.