Nuuk, Greenland - A delegation of US senators visited Greenland Monday to "rebuild the trust" shattered by President Donald Trump's threats to annex the Arctic island by force.

Trump has caused alarm among European allies with his repeated hints at seizing the Danish autonomous territory.

"In just a few sentences and words, trust that has been built since World War II has been eroded and degraded," Republican Senator Lisa Murkowski said at a press conference.

"We need to work to rebuild that trust."

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The delegation also included Independent Angus King, and Democrats Gary Peters and Maggie Hassan, who visited a US military base in Pituffik, and met with Greenlandic Prime Minister Jens-Frederik Nielsen.

They are also set to speak with the island's foreign minister, Vivian Motzfeldt.

Last month, Trump partially backed off threats of military action, claiming he had agreed a "framework" deal with NATO chief Mark Rutte to ensure greater US influence.

A US-Denmark-Greenland working group has been established to discuss Washington's ostensible security concerns in the Arctic, but details have not been made public.

"We have a president that has broken that trust... I think in a significant way, and we now have to repair it," said Peters.

"We consider you friends. We want you to consider us your friend."

While Denmark and Greenland have said they share Trump's security concerns over the potential influence of China and Russia, they have insisted that sovereignty and territorial integrity are a "red line" in the discussions.