The US president tweeted he will postpone an August meeting with Danish Prime Minister Mette Frederiksen as she had no interest in "discussing the purchase of Greenland" with him.
The world’s largest island has long been on the mind of successive American leaders who have been interested in its strategic and economic value.
As Europe lurches to the right, policies that were once rejected by the left are being incorporated into manifestos to garner votes.
Polling stations open at 8 am (0600 GMT) and close at 8 pm, followed immediately by two exit polls. The focus will be on challenges in the Nordic country's welfare model and on two new far-right anti-immigrant parties.
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