"For national security and freedom throughout the world, the USA believes that ownership and control of Greenland is an absolute necessity", writes Trump on his platform Truth Social.
Greenland is a highly self-governing part of Denmark.
Trump does not specify whether it must involve American control. He does not mention buying Greenland, which Trump did propose as president in 2019.
The idea was dismissed as absurd by Denmark's Prime Minister Mette Frederiksen, which led Trump to cancel a state visit to Copenhagen.
Frederiksen also rejects the proposal now and writes to Ritzau that she has no comments, referring to what the government of Greenland has said about Greenland not being for sale, but open to cooperation.
Greenland has a defense agreement with the USA, which gives American military great leeway. There are, among other things, radar stations that provide the opportunity to monitor the airspace over the North Ice Sea.
Trump's statement was made in connection with his appointment of 49-year-old entrepreneur Ken Howery as the USA's future ambassador to Denmark. About the incoming ambassador, who previously was the USA's ambassador to Sweden, Trump writes:
"Ken will do a fantastic job of representing the United States' interests."