The visit to the US military base at Pituffik in the north of the Arctic island comes just hours after a new broad government coalition, which aims to keep ties with Denmark for now, was presented in the capital Nuuk.
Vance greeted members of the US armed forces shortly after his arrival, thanking them for their service on the remote base located 1200 km north of the Arctic Circle.
"The president is really interested in Arctic security, as you all know, and it's only going to get bigger over the coming decades," Vance said.
"It's cold as shit here. Nobody told me," Vance said, prompting laughs, adding it was his first visit to the island. The outside temperature at Pituffik was minus 19 C.
Greenland's new prime minister said the US visit signalled a "lack of respect" and called for unity in the face of "pressure from outside".
Denmark's king issued a statement of support on social media. "We live in an altered reality. There should be no doubt that my love for Greenland and my connectedness to the people of Greenland are intact," King Frederik said.
The US delegation also includes Vance's wife Usha, national security adviser Mike Waltz and Energy Secretary Chris Wright.
The initial plan for the trip had been for Vance's wife to visit a dog-sled race on the island together with Waltz, even though they were not invited by authorities in either Greenland or Denmark.
Public protests and outrage from authorities in both Greenland and Denmark prompted the US delegation to only fly to the military base and not meet the public.
Under the terms of a 1951 agreement, the US is entitled to visit its base whenever it wants, as long as it notifies Greenland and Copenhagen. Pituffik is located along the shortest route from Europe to North America and is vital for the US ballistic missile warning system.
Trump reiterated his desire to take over Greenland as recently as Wednesday, saying the US needs the strategically located island for national and international security.
"So, I think we'll go as far as we have to go. We need Greenland and the world needs us to have Greenland, including Denmark," he said.
The island, whose capital is closer to New York than the Danish capital Copenhagen, boasts mineral, oil and natural gas wealth, but development has been slow and the mining sector has seen very limited US investment. Mining companies operating in Greenland are mostly Australian, Canadian or British.
A White House official has said Greenland has an ample supply of rare earth minerals that would power the next generation of the US economy.
Greenland's new Prime Minister Jens-Frederik Nielsen on Friday urged political unity.
"At a time when we as a people are under pressure, we must stand together," Nielsen said at a press conference.
Danish Prime Minister Mette Frederiksen, who had called the initial plans for the US visit "unacceptable", congratulated Greenland on its new government in a post on Instagram: "I look forward to close cooperation in an unnecessarily conflict-ridden time."
