The latest agreement between the US Trump administration, Denmark and Greenland is likely to affect where Inuit people live, hunt, travel and possibly exercise its own self-government, a former Greenland Prime Minister says.

The White House was quick to declare victory amid US President Donald Trump's long-running desire to increase his government's sway over the Arctic circle, even though the deal fell short of an ambitious conquest over the Danish territory.

Reports overnight indicate an expansion of the US military presence with a further two bases in the small Narsarsuaq settlement and the Mestersvig outpost in Greenland / Kalaallit Nunaat, alongside the preexisting Pituffik Space Base.

Múte Bourup Egede, Minister for Foreign Affairs, Business and Mineral Resources and leader of Inuit Ataqatigiit, Greenland's democratic socialist party, posted on his own Facebook page, selling the benefits of the deal.

"We have now reached a point where an agreement between Greenland, Denmark and United States is within reach: an agreement that recognises Greenland's position and the right to self-determination," the Inuit former Prime Minister wrote.

"(It) strengthens cooperation between our three countries.

"A solution that is good for all parties - and that strengthens the security of the United States, Greenland and the entire Western alliance."

However, Mr Egede concedes the additional military facilities are set to restrict access to land and surrounding areas which Inuit communities use for hunting and traditional travel.

The move will affect subsistence hunting, which remains both culturally and economically significant for Greenland's only Indigenous people.

The 2004 US-Denmark defence arrangements, under Greenland's home rule government status, explicitly required consultation concerning military activities which could affect the Inuit's hunting and environmental areas.

It amended and supplemented the 1951 Defence agreement concerning the territory's defence.

However Mr Egede last year conceded Greenland is part of the North American continent, and "a place that the Americans see as part of their world".

There remains concern over the changes to the Narsarsuaq community over whether its Indigenous character will change and what requirements or restrictions will accompany its new base.

Storch Lund, whose grandfather was the poet that wrote the lyrics to Greenland's anthem, has grown up on a farm across the fjord, fears the worst.

"The requirements could become so extensive that in the end we will have to leave our homes," he told reporters recently.

More aircraft, construction, vehicles and military infrastructure could increase pressure on fragile Arctic ecosystems against the existing defence framework, recognising a need to protect Greenland's environment and hunting areas when military operations occur.

The biggest political issue is self-determination for Inuit peoples who make up approximately 89 per cent of the 56,500 residents in the territory.

The US president has described the new arrangement of giving the Americans a permanent control over Greenland's security.

A larger military presence could bring construction, contracts, jobs and infrastructure, but the Inuit communities have to weigh up those benefits against potential restrictions from the increased militarisation of their traditional land.

There is a long history behind Inuit concerns over US military activity.

The Americans have maintained a major presence at Pituffik since the Cold War to keep the threat of Soviet expansion at bay, amid handing the US broad rights to operate military installations in Greenland.