Kristersson said in a speech on Sunday that the rules-based world order was under greater threat than for many decades.
"We are highly critical of what the United States is now doing and has done in Venezuela in regards to international law and probably even more critical of the rhetoric that is being expressed against Greenland and Denmark," he said at an annual security conference in northern Sweden.
"On the contrary, the United States should thank Denmark, which has been a very loyal ally over the years."
Greenland, home to fewer than 57,000 people and about four-fifths covered by ice, is largely autonomous but formally part of the Kingdom of Denmark, a member of the NATO military alliance.
Trump said on Friday that the US needs to own Greenland to prevent Russia or China from occupying it in the future.
He has repeatedly said that Russian and Chinese vessels are operating near Greenland, something Nordic countries have rejected.
Danish Prime Minister Mette Frederiksen confirmed on Sunday that her Foreign Minister, Lars Løkke Rasmussen, will meet with US Secretary of State Marco Rubio for talks on Greenland next week.
"We are at a crossroads," Frederiksen said during a party conference, according to the Ritzau news agency.
She did not specify a location or exact time for the meeting.
Rubio had previously said he planned to meet Danish representatives next week after Denmark and Greenland requested talks with the top US diplomat.
Frederiksen has warned that if the United States turns its back on NATO co-operation by threatening an ally, then "everything stops".
US President Donald Trump has reiterated his long-held desire to "own" Greenland in recent days, and his administration has not ruled out using military force to gain control, citing security interests and a perceived threat from China and Russia in the region.
with DPA
19°C