Over the past two days, President-elect Donald J. Trump has made clear that he has designs for American territorial expansion, declaring that the United States 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.

Mr. 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 defense affairs — Mr. 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,” Mr. 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.