The new figure from Denmark's SSI infectious diseases agency was slightly above the previous record set on Monday, dashing hopes that the country's second wave of infections had already peaked.
The record came at the same time as the country carried out 71,059 tests in a single day, setting another record.
Of these, 1.7 percent were positive for Covid-19, more or less level with the 1.8 percent registered on Thursday.
At the same time, there were 33 new patients admitted to hospital with the virus, three new deaths and 25 patients discharged, increasing the total number currently being treated in hospital by five to 144.
The total death toll from coronavirus in Denmark is now 719.
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Of Denmark's municipalities, 93 are now over the 'safe' limit of 20 infected per 100,000 inhabitants, with the 11 worst-affected all around the capital of Copenhagen.
The worst-hit municipality is currently Høje Tåstrup, on the outskirts of the capital, with 452 infected per 100,000 over the last week.
Although the number of new infections registered is higher than in the spring, testing levels today are much higher, meaning the real level of infections then was probably several times higher in spring, with 535 people treated in hospital at peak.