"I thought that the Prime Minister's statement was nasty," Trump told the press on Wednesday, referring to Danish Prime Minister Mette Frederiksen, Xinhua reported.
"It was an inappropriate statement. All she has to do is say 'no, we wouldn't be interested'," Trump said.
"Because she's not talking to me, she's talking to the United States of America. You don't talk to the United States that way, at least not under me," he added.
US news outlets recently cited official sources as saying that Trump had considered making a bid to purchase Greenland, an idea Trump later confirmed.
Trump said Greenland had strategic interest for the US, defending his position by saying that previous US Presidents had also floated the idea.
In a stern response, Frederiksen called the idea "absurd," triggering a backlash from Trump.
Trump later continued the rant on Twitter, blasting Copenhagen for not spending enough on military as a member of the North Atlantic Treaty Organisation (NATO).
"For the record, Denmark is only at 1.35 per cent of GDP for NATO spending. They are a wealthy country and should be at 2 per cent," Trump tweeted.
"These countries have agreed to pay ONE HUNDRED BILLION DOLLARS more but still way short of what they should pay for the incredible military protection provided," read another tweet.
Trump on Tuesday announced postponing a scheduled visit to Denmark in early September.
( With inputs from IANS )