The visit comes after high-level talks in Washington failed to dissuade Trump from his plan to annex the semi-autonomous Danish territory.
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The 11-member delegation is meeting MPs as well as Danish Prime Minister Mette Frederiksen and her Greenlandic counterpart Jens-Frederik Nielsen.
The visit comes days after high-level talks in Washington failed to dissuade Trump from his plans.
He insists Greenland is vital for US security - and that Denmark cannot defend it against possible Russian or Chinese attacks. Both Denmark and Greenland say they are opposed to a US takeover.
Greenland is sparsely-populated but resource-rich and its 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.
The US already has more than 100 military personnel permanently stationed at its Pituffik base - 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 has said the US needs to "own" it to defend it properly.
He has consistently offered to buy it off - an offer rejected by Denmark and Greenland - whilst mooting the possibility of seizing it by force.
Denmark has warned that military action would spell the end of Nato - the trans-Atlantic defence alliance where the US is the most influential partner.
Nato works on the principle that allies have to aid each other in case of attack from outside - it has never faced an option where one member would use force against another.
European allies have rallied to Denmark's support.
They have also said the Arctic region is equally important to them and that its security should be a joint Nato responsibility - with the US involved.
To this end, several countries including France, Germany, Sweden, Norway, Finland, the Net