It is the strongest statement by a leader of the Danish territory since US President Donald Trump renewed plans to annex it.
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Jens-Frederik Nielsen's remark at a joint news conference with Denmark's prime minister is the strongest by a representative of the semi-autonomous Danish territory since US President Donald Trump renewed his plan to annex it.
Trump says the US needs to "own" Greenland to defend against Russia and China. The White House has suggested buying the island, but not ruled out the use of force to annex it.
Denmark is a fellow Nato member and Prime Minister Mette Frederiksen has warned that military force would spell the end of the trans-Atlantic defence alliance.
Watch: BBC asks Trump why US owning Greenland is importantDespite being the most sparsely populated territory, Greenland's location between North America and the Arctic makes it well placed for early warning systems in the event of missile attacks, and for monitoring vessels in the region.
Trump has repeatedly said that Greenland is vital to US national security, claiming without evidence that it was "covered with Russian and Chinese ships all over the place".
The US already has more than 100 military personnel permanently stationed at its Pituffik base in Greenland's north-western tip - a facility that has been operated by the US since World War Two.
Under existing agreements with Denmark, the US has the power to bring as many troops as it wants to Greenland.
But Trump told reporters in Washington last week that a lease agreement was not good enough - the US "had to have ownership" and "Nato's got to understand that".
At the news conference in the Danish capital Copenhagen, Frederiksen did not mince her words as she condemned the "completely unacceptable pressure from our closest ally".
She warned that "there are many indications that the most challenging part is ahead of us".
The Greenlandic prime minister said they w