A headline in Berlingske, a conservative daily, read “The U.S. and Denmark’s relationship has never been this ice-cold. It will have wide-ranging consequences.” A headline on the website of the state broadcaster read, “Trump sends Denmark and the U.S.’s relationship to the freezing point.”

Prime Minister Mette Frederiksen has said she had no interest in discussing the sale of Greenland. “Greenland is not Danish. Greenland belongs to Greenland,” Ms. Frederiksen told a Danish newspaper this week. “I strongly hope that this is not meant seriously.”

Before Mr. Trump canceled his visit, she also told a television reporter on Sunday in Nuuk, the capital of Greenland: “Thankfully, the time where you buy and sell other countries and populations is over. Let’s leave it there.” She also added, “Jokes aside, we would naturally love to have an even closer strategic relationship with the U.S. I, we, consider the U.S. to be our most important ally.”