Trump has advocated for Greenland, a self-governing Danish territory, to become part of the United States, citing its strategic importance and mineral resources. Landry, who took office as governor in January 2024, publicly supports the idea.
"You cannot annex another country. Not even with an argument about international security," Danish Prime Minister Mette Frederiksen and Greenland's Prime Minister Jens-Frederik Nielsen said in a joint statement on Monday.
"Greenland belongs to the Greenlanders and the US shall not take over Greenland."
In a post on Truth Social, Trump wrote: "Jeff understands how essential Greenland is to our National Security, and will strongly advance our Country's Interests for the Safety, Security, and Survival of our Allies, and indeed, the World."
The White House did not respond immediately to requests for comment.
Landry, in a post on X, thanked Trump: "It's an honour to serve ... in this volunteer position to make Greenland a part of the US This in no way affects my position as Governor of Louisiana!"
The Trump administration put further pressure on Copenhagen on Monday, when it suspended leases for five large offshore wind projects being built off the East Coast of the US, including two being developed by Denmark's state-controlled Orsted.
Greenland, a former Danish colony with a population of about 57,000, has the right to declare independence under a 2009 agreement but remains heavily reliant on fishing and Danish subsidies.
Its strategic position between Europe and North America makes it a key site for the US ballistic missile defence system, while its mineral wealth has heightened US interest in reducing reliance on Chinese exports.
Greenland's Nielsen commented on Facebook: "We have woken up again to a new announcement from the US president. This may sound big, but it does not change anything for us. We decide our own future."
Danish Foreign Minister Lars Lokke Rasmussen said on Monday he would summon US Ambassador Kenneth Howery, who had pledged "mutual respect" during a recent visit to Greenland.
"Out of nowhere, there is now a special US presidential representative, who, according to himself, is tasked with taking over Greenland. This is, of course, completely unacceptable," Rasmussen told TV2.
Denmark has sought to repair strained ties with Greenland over the past year, while also trying to ease tensions with the Trump administration by investing in Arctic defence to address US criticisms about inadequate security.
"It is a difficult situation that our allies for a lifetime are putting us in," Prime Minister Frederiksen said in an Instagram post.
