People in Greenland were voting Tuesday in a referendum on whether to establish a self-rule government, moving the Arctic glacial island closer to independence from Denmark.

About 56,000 people — most of whom are Inuit — live in Greenland, which is currently a Danish province. More than half of Greenlanders are eligible to vote in Tuesday's referendum.

Greenlanders are asked to vote on whether they support a proposal that would establish Greenland's right within Denmark's constitution to be recognized as a nation, as well as give Greenlanders control over oil, gas and mineral resources on the island.

If the majority of Greenlanders vote Yes to the proposal, it would also establish a separate police force, courts of law and coast guard. As well, it would make Kalaallisut, or Greenlandic Inuit, the island's official language.

"I think it's so exciting," Aaju Peter, an Iqaluit resident who came to Nunavut from Greenland, told CBC News on Monday.

"When you're in your own home, you should be able to say where the furniture goes, and not have somebody else dictate where the furniture goes."

Greenland became a Danish colony in 1775 and remained that way until 1953, when Denmark revised its constitution and made the island a province.

Under the 1979 Home Rule Act, Greenland got its own parliament and government, and self-determination in health care, schools and social services.

Foreign and military affairs are controlled by Copenhagen, and that would continue under the proposal.

The proposal being voted on Tuesday has been worked out between Greenland and Denmark over the past few years.

Aqqaluk Lynge, president of Greenland's Inuit Circumpolar Council, said Denmark's old colonial system taught Greenlanders that "'We would take care of you.'"

"We don't want that," Lynge said. "We want to take care of ourselves."

The outcome of the referendum is likely to be respected by the Danish government, as it supports greater autonomy for Greenland and a phase-out of an annual Danish subsidy of about 3.5 billion kroner, or about $588 million US, which accounts for two-thirds of the island's economy.

But should the majority of Greenlanders vote Yes in Tuesday's referendum, Denmark would not immediately withdraw that funding. Instead, the proposal calls for a gradual phasing out of the subsidy when the island earns

Steen Ulrik Johannessen, a journalist with the Danish News Agency in Copenhagen, told CBC News that the referendum proposes the transfer of responsibility — and the phasing out of the subsidy — to be done gradually.

"As soon as the oil and minerals give more than $1 billion a year, Denmark would slowly withdraw economically," he said. "This would pave the road to independence."

The proposal would also set new rules on how to split potential oil revenue between Greenland and Denmark. Greenlanders hope to find oil reserves off the western and southern coast of the glacial island, although exploration so far has been unsuccessful.

But while some on the island have said Greenland may not yet be ready for more independence, polls indicate most Greenlanders will likely vote Yes on Tuesday.

"To have an identity is so important that I think that a vast majority of Greenlanders will say Yes," Lynge said.