Denmark is as of Saturday open for travel to and from all but six European countries based on coronavirus infection rates, the Danish Foreign Ministry said.
The limit would at most be 20 new coronavirus infections per 100,000 inhabitants a week, thereby excluding Britain, Ireland, Malta, Portugal, Romania, and most of neighbouring Sweden.
"The easing of the travel warnings show that both Denmark and most of Europe are in a far better position than we had dared hope for until very recently," Foreign Minister Jeppe Kofod said on Thursday.
The list would be updated weekly.
Travellers from some Swedish regions could be eligible to visit under a special provision for the Nordic region based on regional infection rates.
Denmark closed its borders in mid-March as part of measures to stem the spread of the virus, but has gradually eased the restrictions.
Norway's Prime Minister Erna Solberg, meanwhile, said in Oslo that travellers to and from most of the Schengen free movement area and the European Economic Area (EEA) were from July 15 to be able to travel to Norway, if virus rates remain low.
The Norwegian Institute of Public Health was by July 10 to compile a list of eligible countries and regions, which would be updated every two weeks.
The criteria include the number of infections compared to the population.
Requirements to self-isolate for 10 days on return to Norway from eligible countries could be dropped.
Norwegians who travel to neighbouring Sweden, which is still struggling with a relatively high case load, will have to continue to self-isolate.