Frederiksen, who had been due to hold talks with Trump in Copenhagen, was unavailable for comment as she was travelling after a visit to Greenland and Iceland this week. "We're working with Democrats, we're working with Republicans".
"(Trump's cancellation) is very, very shocking, when it is about a very close ally and a good friend", Soren Espersen of the hard right Danish People's Party said. So they carry it at a great loss.
"Wayne agrees things have to be done also", Trump added.
"You don't talk to the USA that way", Trump said.
In Greenland, Johannes Kyed, an employee with a mine company, told Denmark's TV2 channel that wanting to buy a country and its people is a relic of the past.
Carla Sands, the USA ambassador to Denmark, had tweeted on Tuesday afternoon that "Denmark is ready" for Mr Trump, adding the words "partner, ally, friend!"
"Our desire for a more strategic and stronger relationship with the U.S. with regard to the Arctic remains completely unaltered, and as such, our invitation for a stronger strategic partnership with the Americans is still open", Frederiksen said in Danish. "Deeply insulting to the people of Greenland and Denmark", tweeted former premier Helle Thorning Schmidt. The president seemed more focused on funding for mental health programs and other topics of interest to the NRA, the people said.
The president has called off a planned visit to Denmark over the dispute. It's where the USA has its northernmost base, Thule, and the island's location close to the natural resources in the Arctic has made it attractive to both Russian Federation and China.
Lars Lokke Rasmussen, the former Danish prime minister, tweeted: "It must be an April Fool's Day joke". "It has gone from a big opportunity for strengthened dialogue between allies to a diplomatic crisis", ex-foreign minister Kristian Jensen of the Liberal Party said.
He then went on to compare purchasing the icy 836,000 square-mile island in the North Atlantic - the world's largest - to a "large real estate deal".
Ms. Frederiksen dismissed the request as "absurd".
Trump's remarks came as he continues to fight with two freshmen Democratic House members - Rashida Tlaib and Ilhan Omar - over what he calls their "hatred" of Jews and Israel.
"There are a number of really terrific countries like Romania, but they have a tremendous corruption problem.
It's the same as President Trump arriving in the United Kingdom and saying he wants to buy Wales or Scotland and I think people feel offended, particularly the people who are part of that nation, in this case the Greenlandic people".
Trump said that he's the "chosen one" to wage a trade war with China and asserted that he's winning. "I am the chosen one".
The Romanian president said such a visit would most likely be possible after the elections in the U.S. Mr. Gifford served as US ambassador to Denmark during the Obama administration.
Additional reporting from Press Association.
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