During a visit to the Arctic territory on Friday, Vance alleged that Denmark was doing too little for the island's security, given the threat from Russia and China in the region.
"Denmark has not kept pace and devoted the resources necessary to keep this base, to keep our troops, and in my view, to keep the people of Greenland safe from a lot of very aggressive incursions from Russia, from China and other nations," Vance said.
Vance gave no details of the alleged incursions.
Greenland is an autonomous Danish territory of 57,000 people which has had self-rule since 2009.
It has long harboured dreams of independence from its former colonial power, but its tiny economy is heavily dependent on fishing and a Danish taxpayer grant.
"This is not how you speak to close allies," Rasmussen said in a rebuke to Vance on X, amid the Trump administration's increasingly aggressive stance on Greenland.
Rasmussen was referring to comments Vance made during a speech to US soldiers at the US base in Pituffik in northwestern Greenland.
Rasmussen maintained that while the Danes are open to criticism: "To be completely honest, we do not appreciate the tone in which it's being delivered".
Although he addressed his words to "our American friends and all others who are listening," he was clearly referring to Vance's speech.
Vance lashed out at Denmark during the prepared speech at the base, saying it has "under-invested" in the territory's people and security.
"Our message to Denmark is very simple: You have not done a good job by the people of Greenland," he said.
"You have under-invested in the people of Greenland and you have under-invested in the security architecture of this incredible, beautiful landmass filled with incredible people."
President Donald Trump has said he wants to bring the resource-rich island under Washington's control "one way or the other," a move that sparked indignation from leaders in Greenland and Denmark.
But a recent poll found 85 per cent of Greenlanders do not want to become part of the US.
Hundreds of protesters demonstrated on Saturday outside the US Embassy in Copenhagen, with some raising signs saying, "back off, USA," Danish broadcaster TV2 reported.
Greenlanders went to the polls earlier in March, and a four-party coalition government was formed on Friday, hours before Vance's visit.
Rasmussen also offered to hold talks on a stronger US military presence in Greenland.
The joint defence agreement of 1951 offers ample opportunities for this, he said.
"If that is what you wish - then let us discuss it," he said.
He described how the US had significantly scaled back its military presence on the island since 1945.
"We can do more. Much more within the framework we have," Rasmussen said.
Specifically in response to Vance's criticism of Copenhagen, he replied: "The fact is that we have all been harvesting the peace dividend. We all acted on the assumption that the Arctic was and should be a low tension area."
"But that time is over. Status quo is not an option," he added.
Denmark has already decided to invest $US1 billion ($A1.6 billion) in Arctic security, Rasmussen said.
It should also not be forgotten that Greenland is part of NATO, he added.
"We live in an altered reality. There should be no doubt that my love for Greenland and my connectedness to the people of Greenland are intact," Danish King Frederik X posted on Facebook.
Between the Arctic and Atlantic oceans, the world's biggest island has been controlled by Denmark for about 300 years.
It governs its own domestic affairs but its foreign and defence policies are formulated in Copenhagen.
with AP
