"I thought the Prime Minister's statement was ... nasty," Trump told reporters at the White House before departing for a veterans' event in Kentucky on Wednesday. "It was an inappropriate statement."
Instead of calling the idea "absurd," Mette Frederiksen should have simply told him her country was not interested in a sale, Trump said.
Frederiksen's comments spurred Trump on Tuesday to cancel his visit to Denmark, a NATO ally, early next month.
During a visit to Greenland, Frederiksen told the newspaper Sermitsiaq: "Greenland is not for sale. Greenland is not Danish. Greenland belongs to Greenland. I strongly hope that this is not meant seriously."
The US president confirmed to reporters on Sunday he had recently discussed the possibility of purchasing the world's largest island, though he said such a move was not an immediate priority.
On Tuesday, he said the US had long pondered purchasing Greenland, and that he considered it a good idea.
White House economic adviser Larry Kudlow has said Greenland is a strategic place and has a lot of valuable minerals.
STRATEGIC LOCATION, RESOURCE WEALTH
Greenland is strategically important for the US military and its ballistic missile early-warning system since the shortest route from Europe to North America runs via the Arctic island. The US maintains an air base in Thule in Greenland's northwest under a 1951 treaty with Denmark.
The island, whose capital Nuuk is closer to New York than the Danish capital Copenhagen, boasts mineral, oil and natural gas wealth. But development has been slow, leaving its economy reliant on fishing and annual subsidies from Denmark.
"It's hurting Denmark very badly because they're losing almost (US) $700 million a year, so they're carrying (Greenland) at a great loss," Trump said.
Greenland lacks basic infrastructure for its tiny population of 56,000. There are no roads between the country's 17 towns and only one commercial international airport, forcing people to travel by sea or air.
Investors from the United States and Canada have been watching for signs Greenland will get a flagging mining programme back on track to exploit vast mineral resources including uranium and rare earths.
However, due to a commodity price slump and a morass of red tape, Greenland - which is three times the size of the large US state of Texas - has only has one small operating mine. Greenland also has an estimated 50 billion barrels of offshore oil and gas reserves, as yet unexploited.
LEGAL OBSTACLES TO SALE
Greenland, once a colony of Denmark, became a formal territory of the Nordic kingdom in 1953 and was granted broad self-governing autonomy, excluding only foreign affairs and defence, under legislation passed a decade ago.
Any sale would require a change to Greenland's legal status through an amendment to Denmark's constitution. Since 2009 Greenland has held the right to declare independence from Denmark. If Greenland do so, it could choose to become associated with the US.
But few Greenlanders see independence as viable given their economic dependence on Denmark, part of the affluent European Union.
