Denmark's prime minister said Wednesday she was "annoyed and surprised" that U.S. President Donald Trump postponed a visit after her government said its territory Greenland was not for sale, but insisted their ties remained strong. 

"I am both annoyed and surprised that the U.S. president has canceled a state visit," Prime Minister Mette Frederiksen told reporters. 

But, she added, "Denmark and the U.S. are not in crisis. The U.S. is one of our closest allies." 

The Scandinavian country's invitation to visit "remains open," she said. 

Trump had tweeted on Tuesday that "based on Prime Minister Mette Frederiksen's comments, that she would have no interest in discussing the purchase of Greenland, I will be postponing our meeting scheduled in two weeks for another time." 

The Wall Street Journal first reported that Trump had expressed interest in the self-governing part of Denmark -- which is mostly covered in ice. 

The president, a former real estate magnate, has been curious about the area's natural resources and geopolitical relevance, the paper said. 

The proposal had sparked both indignation and amusement in Denmark. 

Greenland's foreign affairs ministry said the island was ready to talk business but was not for sale, while Frederiksen has described the idea as "absurd". 

Trump had been scheduled to visit Denmark on September 2 and 3.