Eurosceptic parties the Red-Green Alliance (Enhedslisten) and the Danish People's Party (DF) both characterized the referendum results as a major victory for the British people.
“This will mean that Brits will have better opportunities to decide for themselves and have the right to self-determination closer to the people. That is good for democracy,” Enhedslisten's Pernille Skipper told broadcaster DR.
Enhedslisten said that the referendum results should pave the way for a similar vote in Denmark, and the far-left party called for a Danish referendum within a year.
“We of course hope that this means that here in Denmark we can begin to look at our EU membership and put it to the vote with the Danish people,” Skipper said.
She suggested holding a referendum on Denmark's Constitution Day on June 5th, 2017.
“That would give time to investigate the alternative cooperation possibilities with the EU and especially allow time for a thorough and proper debate amongst the Danish people,” Skipper said.
But Danish PM Lars Løkke Rasmussen, who called the referendum results “very sad […] for Europe and Denmark”, ruled out holding a referendum.
“We belong to the EU and I am not operating on [the belief] that we should have a referendum on that basic question,” Rasmussen said at a Friday morning press conference.
This sets up a potential battle with the Danish People's Party, Rasmussen's largest support party in parliament. DF has previously said that if Brexit becomes reality, Denmark should hold its own EU referendum after the United Kingdom has formally negotiated a post-exit agreement with the union.
On Friday morning, DF spokesman Kenneth Kristensen Berth congratulated Brits for their “brave […] and correct choice” but said a Danish referendum would be dependent on what happens next.
“It's essential that we get an understanding of what the Brits want and we might not have a clear understanding of that already today [Friday]. The Brits have the muscles to negotiate something that is also attractive for Denmark,” Berth told TV2.
Rasmussen, however, said no referendum would happen on his watch – regardless of how the UK formalizes its withdrawal.
“We have the relation to the EU that we have. It is built upon the Danish opt-outs. I don't anticipate a situation in the near future in which we stage a showdown over them,” the PM said.
Denmark has been a reluctant member of the EU since joining in 1973, rejecting the Maastricht Treaty in a 1992 referendum and only saying "yes" the following year after being granted opt-out clauses on the euro, defence, and justice and home affairs.
Danish voters also rejected joining the euro in 2000, and proposals to lift some of the country's exemptions on EU justice rules were turned down in a referendum in December last year.