US Secretary of State Mike Pompeo "expressed appreciation for Denmark's cooperation as one of the United States' allies" in a phone call with Danish foreign minister Jeppe Kofod, a US state department spokesperson said.
The call came after US President Donald Trump snapped back at what he called a "nasty" dismissal from the Danish prime minister at his attempt to purchase Greenland, heightening a row which already prompted Trump to cancel a visit to Denmark next month.
Trump said Prime Minister Mette Frederiksen had "insulted" the US by calling talks of buying Greenland "absurd."
Pompeo called Danish foreign minister Jeppe Kofod to discuss the "postponement" of Trump's visit.
Trump had cancelled his visit to Denmark after the Danish Prime Minister said she would not discuss selling Greenland to the US.
The Arctic territory is an autonomous part of Denmark but is physically part of the North American continent.
"The Prime Minister was able to save a great deal of expense and effort for both the United States and Denmark by being so direct. I thank her for that and look forward to rescheduling sometime in the future!" he continued on Twitter.
The US President and First Lady were set to visit Denmark in early September, having accepted an invitation from the Queen of Denmark.
Trump confirmed to reporters on Sunday that he was "strategically" interested in a deal to buy Greenland.
He subsequently tweeted a doctored picture of Trump Tower in Greenland. He characterised his idea of buying Greenland as essentially "a large real estate" deal. He argued that the island is a burden on Denmark's economy because the territory depends heavily on subsidies from Copenhagen.
Many people thought the idea was a joke.
Danish prime minister Mette Frederiksen commented during a visit to the territory: "Greenland is not for sale. Greenland is not Danish. Greenland belongs to Greenland. I strongly hope that this is not meant seriously."
The territory's ministry of foreign affairs also tweeted on Friday that the territory was "open for business, not for sale."
Speaking to reporters outside the White House on Wednesday, Trump said: "The prime minister (Frederiksen) used a terrible word when talking about something we've been talking about for years."
"It was not a nice statement the way she blew me off. We've done a lot for Denmark ... She said absurd. That's not the right word to use.
"It was not a nice way of doing it. She could have just said no, we'd rather not do it.
"She's not talking to me, she's talking to the United States of America."