"It is very, very shocking, when it is about a very close ally and a good friend," Soren Espersen, the foreign affairs spokesman for the hard right Danish People's Party, told Danish news agency Ritzau.
He described Trump's cancellation as an offence to Queen Margrethe, Denmark's head of state, and that he did not expect another visit by the U.S. president would happen.
Donald Trump and First Lady Melania Trump were formally invited to Denmark by Queen Margrethe in July.
"It shows why we now more than ever should consider (fellow) European Union countries as our closest allies. The man is unpredictable," said Morten Ostergaard, leader of the Danish Social Liberal Party. "Reality surpasses imagination."
Trump, whose "America First" policies have resulted in strained relations with the EU over trade and other issues, said on Sunday that a U.S. purchase of Greenland would be "a large real estate deal", though not an immediate priority.
"Denmark is a very special country with incredible people, but 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," Trump tweeted on Tuesday.
Greenland, which is gaining attention from world powers including China, Russia and the United States due to its strategic location and mineral resources, is self-governing but depends on Denmark for economic support.
Aaja Chemnitz Larsen, a lawmaker from Greenland's opposition party Inuit Ataqatigiit party, said she was not surprised at the cancellation but it underlined the territory's importance.
"The U.S. is an interesting ally for Greenland, but we also wish for Greenland to remain in the union we have today," she told Reuters.
