In 2010, American officials estimated that Afghanistan had untapped mineral deposits worth nearly $1 trillion, an estimate that was widely disputed at the time and has certainly fallen since, given the eroding price of commodities. But the $1 trillion figure is circulating again inside the White House, according to officials, who said it had caught the attention of Mr. Trump.

The lure of Afghanistan as a war-torn Klondike is well established: In 2006, the George W. Bush administration conducted aerial surveys of the country to map its mineral resources. Under President Barack Obama, the Pentagon set up a task force to try to build a mining industry in Afghanistan — a challenge that was stymied by rampant corruption, as well as security problems and the lack of roads, bridges or railroads.

None of these hurdles has been removed in the last eight years, according to former officials, and some have worsened. They warn that the Trump administration is fooling itself if it believes that extracting minerals is a panacea for Afghanistan’s myriad ills.

“It would be dangerous to use the potential for resource exploitation as a selling point for military engagement,” said Laurel Miller, a senior analyst at RAND who served until last month as the State Department’s special representative for Afghanistan and Pakistan. “The barriers to entry are really quite considerable, and that kind of argument could fuel suspicion about America’s real intentions in Afghanistan.”

But for Mr. Trump, as a businessman, it is arguably the only appealing thing about Afghanistan. Officials said he viewed mining as a “win-win” that could boost that country’s economy, generate jobs for Americans and give the United States a valuable new beachhead in the market for rare-earth minerals, which has been all but monopolized by China.