President Trump’s intense interest in Ukraine’s minerals seemed to come from out of the blue.

He dispatched his Treasury secretary to Kyiv this month to negotiate with Ukraine’s leader, then began ratcheting up the pressure publicly in what appeared to critics like a Mafia don’s extortion scheme.

“I want security of the rare earth,” he said.

But critical minerals have been on Mr. Trump’s mind since at least 2017, when he signed an executive order on them during his first term. They also caught the attention of President Joseph R. Biden Jr.

And Mr. Trump’s recent comments on Ukraine’s assets were not the first time in his new term that he has mentioned taking over a country’s mineral holdings.

The president has talked about acquiring minerals in Greenland and Canada. Prime Minister Justin Trudeau of Canada told a group of business leaders that Mr. Trump’s focus on Canada’s minerals meant his threats to annex the country were “a real thing.”

Seizing mineral wealth overseas has become a core foreign policy goal of Mr. Trump’s and an impetus for his most imperialistic remarks since taking office. His instincts hark back to the drives of fallen empires, when resource extraction motivated rulers to expand territory.

On Tuesday, after nearly two weeks of difficult talks, Ukrainian and U.S. officials said they had reached agreement on a framework for sharing revenue from Ukraine’s critical minerals.