To Ukraine, they are a chit to play in an ongoing appeal to President Trump for more financial and military support. To Mr. Trump, they should be overdue payment for billions of dollars committed to Kyiv’s war effort.

Either way, Ukraine’s vast and valuable mineral resources have suddenly become a prominent component in the maneuvering over the country’s future.

Over the past week, Mr. Trump has repeatedly pushed the idea of trading U.S. aid for Ukraine’s critical minerals. He told Fox News on Monday that he wanted “the equivalent of like $500 billion worth of rare earths,” a group of minerals crucial for many high-tech products, in exchange for American aid. Ukraine had “essentially agreed to do that,” he said.

For Ukraine, it is a hopeful sign that Mr. Trump, a longtime skeptic of American aid to Kyiv, might find a path to maintaining support that he finds palatable. But it’s still possible that the famously mercurial president will change his mind, and even his statements about a deal have been ambiguous about whether he wants Ukraine’s minerals for past or future aid — or a combination of both.

Mr. Trump’s proposal followed a campaign launched by Kyiv in the fall to appeal to the U.S. president’s business-oriented mind-set by discussing lucrative energy deals and emphasizing that defending Ukraine aligned with American economic interests.

The campaign included a meeting between Mr. Trump and President Volodymyr Zelensky and trips to the United States by Ukrainian officials to pitch deals for exploiting deposits of lithium and titanium — vital for producing technologies like electric batteries. It also involved getting backing from influential political figures like the Republican senator Lindsey Graham.