The election to the 31-seat Inatsisartut parliament on Tuesday could potentially enhance US influence in Greenland, a sparsely populated island in the eye of a geopolitical race for dominance in the Arctic, as global warming melts the ice caps making its resources more accessible and opening up new shipping routes.
China and Russia have intensified military activity in the region, with the United States striving to keep pace.
Greenland, a Danish territory since 1953, is three times the size of Texas but with a population of 57,000.
The island gained some autonomy in 1979 when its first parliament was formed, but Copenhagen controls foreign affairs, defence and monetary policy and provides just under $US1 billion a year to the economy.
The local government gained more autonomy in 2009, including the right to declare full independence through a referendum, though has not done so on concern living standards would drop without Denmark's economic support.
The island holds substantial natural resources, including critical minerals such as rare earths used in high-tech industries, ranging from electric vehicles to missile systems.
However, Greenland has been slow to extract them due to environmental concerns, severe weather, and China's near-total control of the sector, which has made it difficult for companies elsewhere to make a profit or secure buyers.
The outcome of the election is uncertain, as no polls or exit polls are expected.
A January poll suggested a majority of Greenland's inhabitants support independence, but are divided over the timing and potential impact on living standards.
Since coming to office in January, Trump has repeatedly expressed interest in acquiring Greenland, rekindling a theme from his prior administration, saying the island is vital to US security interests.
He initially declined to rule out military force, alarming many Greenlanders, although he later softened his stance, stating he would respect the will of the local people and was "ready to invest billions of dollars" if they joined the US.
Prime Minister Mute Bourup Egede has stressed the island is not for sale and advocated for a broad coalition government to resist external pressure.
In an interview aired on Monday by Danish broadcaster DR, he dismissed Trump's offer as disrespectful, expressing willingness to co-operate with other countries instead.
Still, Trump's interest has shaken up the status quo in Greenland and, coupled with the growing pride of the Indigenous people in their Inuit culture, put independence front and centre in the election.
All six main parties, including the ruling Inuit Ataqatigiit and government coalition partner Siumut, support independence but differ on how and when it could be achieved.
