“We must respect the choice that a majority of the British people have made. At the same time, I won't hide the fact that I think it is a very sad result for Europe and for Denmark,” Rasmussen said in a statement.
Rasmussen said that he hoped the UK would still choose some sort of “tight relationship” with the EU but that Denmark's relationship with the union would not be affected by Brexit.
“The British referendum does not change the fact that Denmark belongs in the EU. The EU is Denmark's best opportunity to influence the world that we are a part of for better or worse. We can do some things better along, but we are stronger together. Denmark and the Danish economy are highly dependent on the European community,” 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.
Like his British counterpart David Cameron, Rasmussen wants to curb European migrants' access to child benefits, but with exports accounting for just over half of the country's economic output, only two of Denmark's nine major political parties have expressed support for leaving the bloc completely.
“The three most recent referendums – in the UK, the Netherlands and Denmark – should give paused to thought and action. Amongst the population, there is a scepticism towards the EU. As decision makers in the EU, we must take this seriously,” Rasmussen said.
The Danish PM said he would be eagerly awaiting the British government's announcement on what will come next. Rasmussen and other European leaders will convene at a EU summit next week.