Trump insisted on Wednesday that the United States needed the vast Arctic island for national and international security, and has previously refused to rule out the use of force to get it.
Danish and Greenlandic officials, backed by the European Union, have insisted that will not happen.
In the end, the US visit has been reduced to Vance and his wife Usha visiting the US-run Pituffik Space Base in the northwest of the island.
The vice president angered Danes in early February when he said Denmark was “not doing its job (protecting Greenland), and it’s not being a good ally”.
Key missile defence cog
Known as Thule Air Base until 2023, the base served as a warning post for possible attacks from the Soviet Union during the Cold War.
Vance is “right in that we didn’t meet the American wishes for an increased presence, but we have taken steps towards meeting that wish”, Marc Jacobsen, a senior lecturer at the Royal Danish Defence College, told AFP.
In January, Copenhagen announced that it would allocate almost $2 billion to beef up its presence in the Arctic and north Atlantic.
'Not for sale'
Trump's desire to take over the ice-covered territory, which is seeking independence from Denmark, has been categorically rejected by Greenlanders, their politicians and Danish officials.
While all of Greenland's political parties are in favour of independence, none of them support the idea of joining the United States.
JD Vance's visit comes at a time of political flux in Greenland.
Initially, Vance's wife Usha was supposed to attend a dogsled race in the town of Sisimiut, while various reports suggested US national security adviser Mike Waltz and Energy Secretary Chris Wright would also take part in the visit.
He recalled that the government had not “sent out any invitations for visits, private or official”.
A visit to Greenland by Trump's son Donald Jr on January 7 had also been seen as a provocation.
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