Donald Trump Jr has arrived in Greenland, two weeks after his father repeated his desire for the US to take control of the autonomous Danish territory.
Before his arrival in the capital Nuuk, the US president-elect's son said he was going as a tourist on a "very long, personal, day-trip", to talk to people, and had no meetings planned with government officials.
Ahead of his son's trip, Donald Trump revived a controversy he ignited last month when he said "ownership and control of Greenland is an absolute necessity" for US national security.
During his first term as president, Trump had expressed an interest in buying the Arctic island. He has been rebuffed by Greenland's leaders on both occasions.
"We are not for sale and we will not be for sale," the island's Prime Minister, Mute Egede, said in December. "Greenland belongs to the people of Greenland."
With a population of 57,000, Greenland has wide-ranging autonomy, but its economy is largely dependent on subsidies from Copenhagen and it remains part of the kingdom of Denmark.
Egede had been due to meet King Frederik in Copenhagen on Wednesday, but the meeting was postponed because of what the Greenland prime minister referred to as "calendar gymnastics". Danish reports said the prime minister was still due to travel to Copenhagen on Tuesday.
The Danish government has said little about the president-elect's son's visit.
Defence Minister Troels Lund Poulsen said he agreed with Mute Egede's statement that Greenland was not for sale, and the foreign ministry made clear it was not an official trip.
"We have noted the planned visit of Donald Trump Jr to Greenland. As it is not an official American visit, the Ministry of Foreign Affairs of Denmark has no further comment to the visit," the ministry told BBC News.
However, several opposition politicians have expressed concern.
Conservative MP Rasmus Jarlov posted on social media in English that "this level of disrespect from the coming US president towards very, very loyal allies and friends is record-setting".
President-elect Trump said earlier on his Truth Social social media platform that his son, and "various representatives", would travel to Greenland "to visit some of the most magnificent areas and sights".
Trump added that Greenland and its people "will benefit tremendously if, and when, it becomes part of our nation".
"We will protect it, and cherish it, from a very vicious outside world," he said. "Make Greenland great again!"
Before leaving on board his father's private jet, nicknamed Trump Force One, Donald Trump Jr, 47, said on his podcast Triggered, "no, I am not buying Greenland" - although he said he did love it there.
The president-elect's post also included a video featuring an unnamed Greenlander- wearing a red Make America Great Again hat - telling Trump to buy Greenland and free it from "being colonised" by Denmark.
The identity of the man in the clip is unclear.
Greenland lies on the shortest route from North America to Europe, making it strategically important for the US. It is also home to a large American space facility.
The president-elect's eldest son played a key role during the 2024 US election campaign, frequently appearing at rallies and in the media.
Hours after President-elect Trump repeated his interest in buying Greenland last month, the Danish government announced a huge boost in defence spending for the island. Danish Defence Minister Troels Lund Poulsen described the announcement's timing as an "irony of fate".
On Monday, King Frederik X changed the royal coat of arms to more prominently feature representations of Greenland and the Faroe Islands.
Some have seen this as a rebuke to Trump, but it could also prove controversial with Greenland's separatist movement.
King Frederik used his New Year's address to say the Kingdom of Denmark was united "all the way to Greenland", adding "we belong together".
But Greenland's prime minister used his own New Year's speech to push for independence from Denmark, saying the island must break free from "the shackles of colonialism".
Trump is not the first US president to suggest buying Greenland. The idea was first mooted by the country's 17th president, Andrew Johnson, during the 1860s.
Separately in recent weeks, Trump has threatened to reassert control over the Panama Canal, one of the world's most important waterways. He has accused Panama of charging excessive fees for access to it.
Panama's president responded by saying "every square metre" of the canal and surrounding area belonged to his country.