US President Donald Trump insisted earlier this year that Washington needed to control Greenland for national security reasons, though he ultimately ruled out annexing it by force.
Trump argued that Denmark has not invested enough in Greenland and said the island's strategic importance is growing as China and Russia expand their presence in the Arctic.
Frederiksen said Denmark is "ready to defend every inch of NATO including our own territory" in the event of an attack, and would rely on NATO allies to honor their commitment to defend each other.
More than 4.3 million people are eligible to have their say in the vote for the new Folketing, or parliament, in Copenhagen, which is elected for a four-year term.
Prime Minister Mette Frederiksen called the election last month, apparently hoping that her straight-talking image in the Greenland crisis would win her points with the electorate.
A day earlier, Trump said he was sending "a great hospital boat to Greenland to take care of the many people who are sick, and not being taken care of there".
