Over the past two days, President-elect Donald J. Trump has made clear that he has designs for American territorial expansion, declaring that the US has both security concerns and commercial interests that can best be addressed by bringing the Panama Canal and Greenland under American control or outright ownership.

Trump’s tone has had none of the trolling jocularity that surrounded his repeated suggestions in recent weeks that Canada should become America’s “51st state”, including his social media references to the country’s beleaguered Prime Minister as “Governor Justin Trudeau”.

Instead, while naming a new ambassador to Denmark — which controls Greenland’s foreign and defence affairs — Trump made clear on Sunday that his first-term offer to buy the landmass could, in the coming term, become a deal the Danes cannot refuse.

He appears to covet Greenland both for its strategic location at a time when the melting of Arctic ice is opening new commercial and naval competition and for its reserves of rare earth minerals needed for advanced technology.

“For purposes of National Security and Freedom throughout the World,” Trump wrote on social media, “the United States of America feels that the ownership and control of Greenland is an absolute necessity”.

On Saturday evening, he had accused Panama of price-gouging American ships traversing the canal, and suggested that unless that changed, he would abandon the Jimmy Carter-era treaty that returned all control of the canal zone to Panama.

“The fees being charged by Panama are ridiculous,” he wrote, just ahead of an increase in the charges scheduled for January 1. “This complete ‘rip-off’ of our country will immediately stop.”

Not surprisingly, the government of Greenland immediately rejected Trump’s demands, as it did in 2019, when he first floated the idea. “Greenland is ours,” Prime Minister Mute B. Egede said in a statement. “We are not for sale and will never be for sale. We must not lose our long struggle for freedom.”

The Danish Prime Minister’s office was more circumspect, writing in a statement that the government was “looking forward to working with the new administration” and offering no further comment on Trump’s remarks.

After Trump brought up the Panama Canal again in a speech on Sunday, Panama’s President, José Raúl Mulino, said in a video that “every square metre of the Panama Canal and its adjacent zones is part of Panama, and it will continue to be”. He added: “Our country’s sovereignty and independence are not negotiable.”

Trump’s aggressive interpretation of the phrase evokes the expansionism, or colonialism, of President Theodore Roosevelt, who cemented control of the Philippines after the Spanish-American War. And it reflects the instincts of a real estate developer who suddenly has the power of the world’s largest military to back up his negotiating strategy.

In the cases of Greenland and Panama, both commercial and national security interests are at play.

Trump’s desire for Greenland was made explicit in the first term, when a wealthy New York friend of his, Ronald S. Lauder, the New York cosmetics heir, put the idea in his head.

In the Trump White House in 2019, the National Security Council was suddenly delving into the details of how the US would pull off a land acquisition of that size. Trump kept pressing the point with Denmark, which consistently rebuffed him.

Trump was not the first President to make the case: Harry S. Truman wanted to buy Greenland after World War II, as part of a Cold War strategy for boxing out Soviet forces. Trump can make a parallel argument, especially as Russia, China and the US jockey for control of Arctic routes for commercial shipping and naval assets.

Arctic experts did not dismiss Trump’s Greenland bid as a joke.

“Not that many people are laughing about it now,” said Marc Jacobsen, an associate professor at the Royal Danish Defence College in Denmark who focuses on Arctic security.

Jacobsen noted that the reaction in Denmark to Trump’s latest bid had been one of fury (one Danish politician called it “an unusually strange way to be an ally”). But, he said, Greenlanders — who have long sought independence — may seek to use Trump’s interest as an opportunity to further strengthen economic ties with the US.

Since 2009, Greenland has had the right to declare its independence, but the vast territory of about 56,000 people is still heavily dependent on Denmark and has never chosen to pursue that path. Trump’s interest could give Greenland an opening for more US investments, including in tourism or rare earth mining, he said.

“Was it crazy when the US acquired Alaska? Was it crazy when the US built the Panama Canal?” asked Sherri Goodman, a former Pentagon official and a senior fellow with the Wilson Center Polar Institute, a Washington-based think tank.

Goodman said the US did have a strong interest in ensuring that China in particular does not develop a strong presence in Greenland.

Beijing’s ambitions in the Arctic have grown, and in 2018 it laid out plans to build infrastructure and develop shipping lanes opened by climate change. Goodman said the US should continue to prevent China from gaining a foothold in the doorstep to North America, but said Greenlanders must decide their own fate.

David L. Goldwyn, who served at the state department under Presidents Bill Clinton and Barack Obama, noted that Greenland has tremendous undeveloped natural resources, including more than 43 of the 50 so-called critical rare earth elements used to make electric vehicles, wind turbines and other clean technology.