Around one in 16 people in Scotland had coronavirus in the week to July 7, according to the infection survey produced by the Office for National Statistics (ONS).
This equates to around 334,000 people.
Covid-19 remains most prevalent in Scotland, the ONS said, after cases increased from the 312,800 reported last week.
Elsewhere, Wales saw infections jump to around one in 17 of its population, while England reported cases in around one in 19.
Cases in Northern Ireland were also seen in around one in 17 people.
Data for Wales, England and Northern Ireland covered the week ending July 6.
Sarah Crofts, head of analytical outputs for the ONS Covid-19 Infection Survey, said: “Infections are showing no signs of decreasing, with rates approaching levels last seen in March this year at the peak of the Omicron BA.2 wave.
“Rates have continued to increase across the UK and among all age groups. We will continue to closely monitor the data.”
Patients numbers in Scotland, Wales and Northern Ireland are currently around three-quarters of the peak reached during the BA.2 wave.
Around six in 10 hospital patients who test positive for Covid-19 are being treated primarily for something else, rather than the virus.
But they will need to be kept isolated from those patients who do not have Covid, putting extra pressure on hospital staff who are already struggling to clear a record backlog of treatment.
The UK’s full Covid-19 death toll was confirmed earlier this week as having passed 200,000.
A total of 200,247 people have now had coronavirus recorded on their death certificate since the pandemic began, according to the ONS.
This includes all instances where Covid-19 has been mentioned on someone’s death certificate, either as a main cause of death or a contributory factor.
Deaths involving coronavirus have remained low by historic standards during each of this year’s waves, reflecting the success of vaccines in weakening the link between infection and serious illness.