Mr. Trump has been explicit about his expectations for his new ambassador filling a once-sleepy post. When he announced Mr. Howery for the role, which requires Senate confirmation, he reiterated his designs on Greenland for the first time since winning the presidency.

Thanking Mr. Trump on X, Mr. Howery mentioned not just the U.S. Embassy in Copenhagen but also the U.S. Consulate in Nuuk, Greenland, saying he was eager to “deepen the bonds between our countries.”

On cue, Mr. Musk chimed in: “Congrats! Help America gain Greenland.”