"We have fought side by side with the Americans for many, many decades. We are one of the United States' most important and best allies -- and that's why I don't want Denmark to be labelled a bad ally," Frederiksen told reporters in Brussels.
US President Donald Trump has repeatedly signalled that he wants the Arctic island -- which holds a strategic importance and is believed to hold large untapped mineral and oil reserves -- to become part of the United States.
In an interview with broadcaster Fox News over the weekend, Vance said that Greenland was "really important" to US "national security".
"Frankly, Denmark, which controls Greenland, it's not doing its job, and it's not being a good ally," Vance said.
A day after Trump was sworn in as president, Greenland Prime Minister Mute Egede insisted that Greenlanders "don't want to be American".
Frederiksen on Monday stressed that Denmark would continue to seek a strong relationship with the United States.
"We will do what we can to influence the Americans to continue the good co-operation," Frederiksen said.
Frederiksen recently commented on a similar topic, when she stressed that Denmark is, and intends to remain, an ally of the US. Denmark was part of the US-led coalition during the war in Afghanistan, where 43 Danish soldiers lost their lives between 2002 and 2021.
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