Denmark will close middle and high schools, bars, cafes and restaurants in 38 municipalities this week in new shutdown measures set to affect almost half of the country's population, the government said Monday.

The spread of the infection "is too high and the situation is too worrying. As a result, we have to adopt measures to control the infection and the epidemic," Prime Minister Mette Frederiksen told reporters.

She also urged Danes to limit their Christmas and New Year's gatherings to 10 people.

As in the first wave at the start of the year, middle and high schools will return to distance learning from Wednesday, when bars, cafes and restaurants also have to close for eat-in diners, though takeaway will be allowed.

Libraries, gyms, cinemas and theatres also have to shut down.

Denmark avoided shutdowns in October and November when many other European economies closed shops and restaurants to stem the spread of Covid-19.

The restrictions will be in place until January 3, with Health Minister Magnus Heunicke qualifying the rising infection rate as "exponential".

Public health officials on Monday registered a daily record of 2,046 cases in 24 hours, expressing concern that they could rise to 4,000 a day by Christmas in the country of 5.8 million, public television DR reported.

The new measures will be introduced in Denmark's most affected areas, including the capital Copenhagen and its suburbs, the western city of Aarhus and the central town of Odense, which together are home to almost half of the Danish population.

The Scandinavian country, which is struggling to contain the virus, had already last week reduced the limit on children's extra-curricular activities from 50 to 10 and urged people in Copenhagen to increasingly work from home.