"The level of contagion in society is still very low," the Danish health authority said in a report in Wednesday, according to Reuters news agency.
It added that the number of confirmed new infections had continued to fall despite more tests being carried out.
In April Denmark became the first country to reopen its schools and daycare centres and the following month bars and restaurants and shopping centres were allowed to resume business.
"There is no sign yet of noticeable changes in the extent of contagion despite the gradual reopening of society in April and early May," the report said.
In its report, the agency calculated that Denmark's 'R number' for the coronavirus pandemic had risen to 1.0 over the last week from a low of 0.7 estimated on May 18.
But Jens Lundgren, a professor of infectious medicine at Copenhagen's leading hospital Rigshospitalet, said that the rise in the R number, which describes the number of people each infected person on average goes on to infect, was less significant when the level of overall infection in society was so low.
"There's nothing dangerous about this. It is an indication that the infection is very low," he told the Ritzau newswire. "I think you have to stop using concepts like reproduction number for the present. Right now, it's fine to have a reproduction number of 1.0 "
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