The Danish government has said it would like to hold a fresh referendum on whether to adopt the euro.
Anders Fogh Rasmussen wants a referendum in the next four years
Back in 2000, the Danish people voted by 53% to 47% not to join the single currency and instead keep the krone.
Prime Minister Anders Fogh Rasmussen, whose centre-right government was re-elected last week, said "the time was approaching" to reassess the euro.
He said he also wanted the referendum to look at ending Denmark's opt-outs in defence, justice and home affairs.
Denmark was granted the four exemptions after voters rejected the Maastricht Treaty in 1992. They adopted the document the following year.
"It is the government's view that the people in this parliamentary term should have the opportunity to take a stance on the Danish EU opt-outs," said Mr Rasmussen.
The referendum will take place at some stage in the next four years, he indicated.
A member of the European Parliament for the opposition Social Democrats, Dan Jorgensen, said his party had been asking for a vote for several years but it was a difficult thing to do in Denmark and its leaders had tended to avoid taking the risk because "the EU is always controversial".
Denmark previously raised the issue of a fresh referendum on the euro in 2003, but it did not come to anything on that occasion.
An opinion poll of 1,000 people published last month in the run-up to the election suggested that 51% of Danes were happy to ditch the opt-out on the euro, and 40% were opposed.
Economic analysts say that as the krone has been tracking the euro, joining the single currency would have minimal impact.
Finland is the only Nordic country to have joined the euro. Sweden rejected the single currency in a referendum in 2003 and Norway is part of the European Economic Area rather than the EU.
The Danish prime minister also said that he wanted his country to ratify the EU reform treaty quickly, but he gave no indication that there would be a referendum on it.
The treaty is due to be signed in Lisbon next month and will then require ratification in all member states.
At a news conference in which he set out his government's priorities for the next four years, Mr Rasmussen said he would try to improve conditions for asylum-seekers and seek to bring down the rate of income tax.
Denmark joined the European Economic Community, the precursor to today's European Union, in 1973, at the same time as the UK and the Republic of Ireland.