Greenland's government lost its parliamentary majority as a row between coalition partners escalated on Monday over how a planned upgrade of three airports, of strategic interest to both Washington and Beijing, should be financed.
Partii Naleraq, a pro-independence party, said on Sunday it was quitting the coalition over a plan for Denmark, whose leader is visiting the capital Nuuk on Monday, to part-fund the project.
The Arctic island is a self-ruling part of Denmark, which is concerned that Chinese investment - on the agenda since Greenland's Prime Minister Kim Kielsen visited Beijing last year - could upset the United States.
In January, Beijing laid out ambitions to form a "Polar Silk Road" by developing shipping lanes opened up by global warming and encouraging enterprises to build infrastructure in the Arctic.
That would imply direct involvement by Denmark in Greenland politics and "we do not want to be part of that", Partii Naleraq said in a letter quoted by local broadcaster KNR.
Its departure leaves Kielsen's coalition, which was formed in May, with only 12 of 31 seats in parliament.
"I will talk to other parties about whether there is a foundation for a new coalition," Kielsen said on KNR. He told newspaper Sermitsiaq that he hoped to avoid having to call a snap election.
Kielsen's Siumut and the two other parties in the coalition, Atassut and Nunatta Qitornai, all back the proposed Danish contribution to the airports.
Opposition party The Democrats said on Sunday they would discuss with Kielsen the possibility of creating a new coalition.
Greenland, itself also eager to benefit from growing activity in the Arctic, plans to expand airports in the capital Nuuk, the tourist hub in Ilulissat and at Qaqortoq in southern Greenland to cater for direct flights from Europe and North America.
Rasmussen said in June that it was the assessment of the Danish government, which still handles the island's foreign and security policy, that the project was of a magnitude to impinge on those areas.
Greenland is strategically important for the U.S. military and its ballistic missile early warning system, as the shortest route from Europe to North America goes via the Arctic island.
According to Kalaallit Airports, a state-owned company set up to build, own and operate the airports, a Chinese construction company has appeared on a list of six firms that have shown interest in the projects, whose costs are estimated at 3.6 billion Danish crowns ($559 million).
Rasmussen did not immediately respond to a Reuters request for comment.
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