GREENLAND is set to have its first woman prime minister after the social democratic Siumut party won general elections on a vow to tax foreign mining companies, final results show.

Aleqa Hammond’s party garnered 42.8 per cent of the vote compared to 26.5 per cent at the last election four years ago. Leftwing incumbent Kuupik Kleist’s Inuit Ataqatigiit took 34.4 per cent compared to 43.7 per cent at the last election.

Hammond, whose party favours taxing foreign companies tapping the island’s vast mineral wealth, said it was clear voters were dissatisfied with the current leadership.

“Too much secrecy surrounding mining projects and problems in the fishery sector, as well as a lack of construction outside Nuuk, determined the outcome,” she told the online edition of weekly newspaper Sermitsiaq.

“We have taken difficult decisions in fisheries, raised rents to be able to afford the necessary renovations, and high unemployment has probably also played a role,” Kleist said of the defeat.

Official turnout figures for the 40,000 island electorate were not immediately available.

Hammond only has to choose one other smaller party for a majority coalition. Negotiations for a new government are expected to take several days.

“I will now be talking to my board before deciding how to move forward,” the 47-year-old party leader told reporters after her victory became official.

Siumut, which fought its election campaign mainly on changing royalty conditions for foreign mining companies wanting to extract rare earth and other raw materials from the potentially rich Greenland underground, is also looking for independence from Denmark for the autonomous territory.

Denmark currently provides 3.2 billion kroner ($A545.84 million) per year in subsidies to Greenland under an autonomy agreement that gives the country full control of its natural resources, while Denmark maintains control of foreign policy and defence.