* Election watched closely by global mining industry
* Greenland has vast deposits of rare earth metals
* Long-dominant ruling party behind in opinion polls (Updates with start of voting)
COPENHAGEN, April 6 (Reuters) - Greenlanders began voting in a parliamentary election on Tuesday that could unseat the ruling political party and help decide the fate of vast deposits of rare earth metals which international companies want to exploit.
The Arctic island of 56,000 people, which former U.S. President Donald Trump offered to buy in 2019 only to be told it was not for sale, is part of the Kingdom of Denmark but has broad autonomy.
International companies are watching the election closely as they compete for the right to develop Greenland's untapped deposits of rare earth metals including neodymium, which is used in wind turbines, electric vehicles and combat aircraft.
Global warming and melting ice have made Greenland more attractive for investment as access by sea has become easier --Trump's offer for Greenland was intended to help address Chinese dominance of rare earth supplies.
But concern in Greenland is mounting about the potential environmental impact of plans to build a large mining complex at Kvanefjeld in the south of the island, a site that contains uranium as well as neodymium.
A junior party withdrew from the coalition government in February as opposition to the project mounted, prompting the decision to call Tuesday's snap election to the 31-seat parliament.
Opinion polls before the election showed the social democrat Siumut Party, which has led all governments since 1979 except for one period between 2009-2013, trailing the main opposition party, Inuit Ataqatigiit (IA).
Support from Siumut helped secure preliminary approval for the Kvanefjeld project, which is licensed to Australian Greenland Minerals, in which Chinese Shenghe Resources is the biggest shareholder.
If IA can form a coalition to govern, it could raise questions about the project. IA has a zero-tolerance policy for uranium and has criticised the project.
Polling stations close at 8 pm (2200 GMT) and deputies will be elected for four years. In the last election in 2018, final results were published about eight hours after polls closed.
Apart from mining, election campaign issues have included housing, the fishing industry and efforts to gain more autonomy.
Greenland's mining potential is widely seen as vital to its prospects of achieving more economic independence, as its $3 billion economy and large public sector are heavily reliant on grants from Denmark.
A majority of Greenlanders view independence from Denmark as a long-term goal but say economic development is needed first.
(Reporting by Nikolaj Skydsgaard, Editing by Timothy Heritage and Gareth Jones)