The figure from national agency State Serum Institute exceeds the total from Monday, which was the existing record, by over 4,000.
The 33,493 cases were found among 193,130 PCR tests, giving a test positivity rate of 17.3 percent, the highest proportion of positive tests seen in one day in Denmark during the pandemic.
However, the number of patients receiving intensive care treatment for Covid-19 fell, continuing a recent decline in that number.
Of 810 patients in Danish hospitals with Covid-19, 49 are admitted to ICUs and 29 are receiving ventilator treatment. Those two figures are at their lowest levels since late November, before the Omicron variant of the coronavirus was dominant in Denmark.
The figure of 810 hospital patients can include people who are admitted to hospital for reasons other than Covid-19, but have also tested positive for the virus.
Prime Minister Mette Frederiksen said on Monday that the country could be in a position to consider easing the current restrictions because the number of patients in intensive care with Covid-19 is declining.
The number of patients in hospital who have Covid (not just ICU patients) has also been stable in recent weeks.
The number of infections and number of hospitalised patients are not as closely correlated as they “once were”, Frederiksen said in an interview with newspaper Ekstra Bladet.
“Of course we are at a place and in a situation where we must re-evaluate not only the current restrictions, of which there are not many remaining, but how we manage the situation in its entirety. That’s certainly what we’re doing in the government now,” she said.