His comments follow renewed interest in the Arctic island by US President Donald Trump.
European powers rallied behind Greenland on Monday, after the US military operation in which Venezuela's leader Nicolas Maduro was seized, rekindling concerns that the island, an autonomous Danish territory, might face a similar scenario.
"We are not in the situation where we are thinking that a takeover of the country might happen overnight," Nielsen said at a news conference in the capital Nuuk, speaking via a translator.
"You cannot compare Greenland to Venezuela. We are a democratic country."
Trump, who said the US was taking temporary control of oil-producing Venezuela, has said repeatedly he wants to take over Greenland and told The Atlantic magazine on Sunday: "We do need Greenland, absolutely. We need it for defence."
Speaking to reporters aboard Air Force One early on Monday, Trump said he would revisit the topic in a few weeks.
In a Facebook post late on Sunday, Nielsen said: "Enough is enough... No more fantasies about annexation."
Denmark's Prime Minister Mette Frederiksen also addressed Trump's comments: "Unfortunately, I think the American president should be taken seriously when he says he wants Greenland," she told public broadcaster DR.
"I have made it very clear where the Kingdom of Denmark stands, and Greenland has repeatedly said that it does not want to be part of the United States."
Greenland, the world's largest island with a population of 57,000 people, is not an independent member of NATO but is covered by Denmark's membership of the Western military alliance, of which the US is also a member.
"If the United States attacks another NATO country, everything stops," Frederiksen said.
Trump appointed Louisiana Governor Jeff Landry as special envoy to Greenland last month. Landry has publicly expressed support for incorporating Greenland into the US.
Greenland's strategic location between Europe and North America makes it a critical site for the US ballistic missile defence system. The island's significant mineral resources also align with Washington's ambition to reduce dependence on Chinese exports.
European allies backed Denmark and Greenland on the matter, emphasising that the island's future lies in the hands of its people.
"Greenland and the Kingdom of Denmark must determine the future of Greenland and nobody else," British Prime Minister Sir Keir Starmer said on Monday.
German Foreign Minister Johann Wadephul suggested NATO could discuss strengthening Greenland's protection, while the European Union reiterated its commitment to the principle of national sovereignty.
