"I think Greenland is going to be something that maybe is in our future," Trump told reporters after a meeting with officials in his Cabinet, saying it was important for US national security.
Greenland's outgoing Prime Minister Mute Egede called plans by the US delegation to visit an American military base and attend a dog sled race a "provocation", and said his caretaker government would not meet with the group.
Trump said his administration was working with "people in Greenland" who want something to happen, but did not elaborate.
"They're calling us," he said. "We're not calling them."
The US visit, which runs from Thursday to Saturday, will be led by Usha Vance, wife of Vice President JD Vance, and include White House National Security Adviser Mike Waltz and Energy Secretary Chris Wright.
Trump has made US annexation of Greenland a major talking point since his eldest son, Donald Trump Jr., paid a private visit to the vast, mineral-rich island in January.
"Until recently, we could trust the Americans, who were our allies and friends, and with whom we enjoyed working closely," Egede told local newspaper Sermitsiaq. "But that time is over."
Naalakkersuisut, the Greenlandic government, is now in a caretaker phase following a March 11 parliamentary election won by the Democrats, a pro-business party that favours a slow approach to independence from Denmark.
Jens-Frederik Nielsen, leader of the Democrats, called for political unity and criticized the timing of the US visit during coalition talks with municipal elections due next week.
"We must not be forced into a power game that we ourselves have not chosen to be a part of," Nielsen said on Monday.
Brian Hughes, spokesman for the White House National Security Council, said the visit aimed to "build on partnerships that respect Greenland's self-determination and advance economic cooperation".
"This is a visit to learn about Greenland, its culture, history, and people and to attend a dogsled race the United States is proud to sponsor, plain and simple," Hughes said.
HEAVY SECURITY
Two US Hercules military transport planes arrived in Greenland's capital Nuuk late on Sunday, carrying security personnel and bulletproof vehicles, Greenlandic online news outlet Sermitsiaq reported.
Around 60 police officers from Denmark also arrived in Nuuk on Sunday, state broadcaster KNR reported.
Waltz and Wright plan to visit the Pituffik space base, the US military base located along the shortest route from Europe to North America, vital for its ballistic missile warning system.
They will then join Vance to visit historical sites and attend the national dog sled race.
Vance said in a video posted by the US consulate in Greenland that her visit was meant to "celebrate the long history of mutual respect and cooperation between our nations".
Trump, who first floated the idea of buying Greenland in 2019, has renewed his calls for the US to take over the island since his return to the White House in January, and he has not ruled out using force to achieve this objective.
Greenland is rich in raw materials, including minerals critical to advance new technologies.
The governments of both Greenland and Denmark have voiced opposition to any US takeover.
Danish Prime Minister Mette Frederiksen said in a written comment reacting to news of the US delegation's visit that "this is something we take seriously".
She said Denmark wanted cooperation with the United States, a NATO ally, but on the basis of "the fundamental rules of sovereignty", adding that Copenhagen and Greenland's future government would both be involved in any talks with the US regarding the island.
