Greenland began voting Tuesday in legislative elections which could yield a timeline for independence for the Danish self-governing territory coveted by US President Donald Trump.

Trump, determined to get his hands on the vast Arctic island "one way or the other", tried until the last minute to influence the election, sparking astonishment, rejection, and, to a small degree, enthusiasm among the 57,000 Greenlanders, most of whom favour independence.

"Our country is in the eye of the storm," Greenland's outgoing Prime Minister Mute Egede, head of the left green party Inuit Ataqatigiit (IA), said in a video posted to Facebook just hours before the vote.

"The international community is watching us closely, and we have recently seen how much they are trying to influence our country," he said.

Polling stations opened at 9:00 am (1100 GMT) and will close at 8:00 pm (2200 GMT), with first results expected several hours later.

The lead-up of the election to choose the 31-seat parliament, the Inatsisartut, was mostly marked by a debate on issues such as healthcare, education, and future ties with Denmark, which still controls foreign, defence and monetary policy.

Greenland's inhabitants -- almost 90 percent of whom are Inuits -- say they are tired of being treated like second-class citizens by their former colonial power, which they accuse of suppressing their culture, carrying out forced sterilisations and removing children from their families.

All of Greenland's main political parties favour independence but they disagree on the timeframe.

Independence now or later?

Some, such as the nationalist Naleraq party, the main opposition faction, want to seek independence quickly.

Others prefer to wait until the island is financially independent, such as the two parties who make up the outgoing coalition, the left-green Inuit Ataqatigiit (IA) and social democratic Siumut.

The island, covered 80 percent by ice, depends on its fisheries sector, which accounts for almost all of its exports, and annual Danish subsidies of more than $565 million, equivalent to a fifth of its GDP.

The most impatient independence backers believe Greenland will soon be able to stand on its own thanks to untapped mineral reserves, including rare earths crucial to the green transition.

But the mining sector is still in its embryonic stages, hampered by high costs due to Greenland's harsh climate and lack of infrastructure.

Trump floated the idea of buying Greenland during his first mandate, in a bid swiftly rejected by Danish and Greenlandic authorities.

Back in the White House, he has circled back on the ambition with greater fervour, refusing to rule out the use of force and invoking US national security.

Late Sunday, Trump invited Greenlanders "to be a part of the Greatest Nation anywhere in the World, the United States of America". He promised in a post on his social network Truth Social to make them "rich".

The most recent polling on the issue, published in January, shows 85 percent of Greenlanders are opposed to Trump's idea.

"We don't want to be American. He is so arrogant," 58-year-old Rene Olsen, a ship repairman, told AFP on Monday.

Yet the statements by Trump -- whom Prime Minister Egede has described as "unpredictable" -- sent a jolt through the election campaign.

Naleraq's nationalists say his remarks have given them leverage ahead of independence negotiations with Denmark.

But Trump's remarks have also chilled some independence supporters, making continued ties with Copenhagen more attractive to them.

More polarisation

A municipal employee in the southern town of Qaqortoq, Kornelia Ane Rungholm, said she did not want "independence today, because Trump will take us as soon as possible".

Political analysts say Trump's meddling in the election contributed to a more polarised debate, by reinforcing each side's convictions, but overall it was not expected to influence the result.

His last message "demonstrates the way the Trump administration insists on interfering in other countries' elections", Danish political scientist Ulrik Pram Gad told AFP.

"But already, after Germany (where Trump's close supporter Elon Musk is backing the far-right AfD party) they should have learned that it's not serving them well," he said.

"The sender of the message is not appealing to the one for whom the message is intended."