Greenland residents took part in a general election on Tuesday that could have massive significance for the Arctic island coveted by United States President Donald Trump.

The mineral-rich territory that has a population of 57,000 has been at the center of a geopolitical race for dominance of the Arctic recently led by the US, which has seemingly been attracted to its plentiful natural resources, which have become more accessible as the ice caps have melted.

With new shipping routes across the Arctic also likely to be up for grabs, Trump has repeatedly said he wants to incorporate Greenland into the US.

Greenland, which is a semi-autonomous territory belonging to Denmark, has sofar shown little interest in Trump's offer.

The island, which is three times the size of Texas, is heavily subsidized by Denmark, which provides military protection and currency, and on Tuesday voters effectively got to choose between sticking with the status quo, becoming fully independent, or trying something new.

The result will be known on Wednesday.

Masaana Egede, editor of the Sermitsiaq, a national newspaper in Greenland, told the Reuters news agency: "The question of independence was put on steroids by Trump. It has put a lid on everyday issues."

Greenland's state broadcaster, KNR, carried a candidates' debate on Monday in which the leaders of the five main political parties taking part in the election all voiced concerns about the US president.

"We don't trust Donald Trump at all," said Erik Jensen, leader of the Siumut party, which was part of the ruling coalition ahead of the vote. "He is trying to influence us. I can understand if citizens feel insecure."

Greenland's Prime Minister Mute Egede has insisted the island is not for sale and told the Danish broadcaster DR that Trump's offer of spending huge amounts of money on its people was disrespectful.

Egede, who leads the Inuit Ataqatigiit party, said the island was facing a "fateful choice", and that the whole world would be watching its outcome.

"The things that are happening in the world right now worry me quite a lot," he said. "That there is a world order that is faltering on many fronts, and perhaps a president in the United States who is very unpredictable in a way that makes people feel insecure. We deserve to be treated with respect, and I don't think the American president has done that lately, since he took office."

Trump, who told Congress last week the US will get its hands on Greenland "one way or the other" has pledged to "invest billions of dollars to create new jobs and make you rich".

But Egede said: "We need to draw a line in the sand and spend more effort on those countries that show us respect for the future we want to draw."

But the pro-independence Naleraq party, which has been the island's main opposition party in recent months, was gaining ground in the run-up to the election, and has said it is willing to work with the US.