Just before Mr. Trump took office, Mr. Luksic added a personal investment to his portfolio: a $5.5 million house in Washington. Mr. Luksic bought the house with the intention of renting it to a wealthy new arrival to Mr. Trump’s Washington, according to Rodrigo Terré, chairman of Mr. Luksic’s family investment office, which handled the purchase.

The idea worked. Even before the purchase was final, real estate agents had lined up renters: Jared Kushner and Ivanka Trump.

The rental arrangement has been a point of concern for ethics experts and groups opposed to mining near the Boundary Waters, and has focused national attention, particularly among some Democrats in Congress, on an otherwise local debate.

The Wall Street Journal first reported about the house in March 2017. At that time, Twin Metals was suing the federal government over the mining leases, but the Trump administration’s direction on the mine since then had only begun to take shape.

In recent months, the scrutiny has grown. In March, Representative Raúl M. Grijalva, the Arizona Democrat who is chairman of the House Natural Resources Committee, wrote a letter with other lawmakers to the interior and agriculture secretaries raising significant concerns about the proposed mine.

The letter said the two departments’ actions “blatantly ignored scientific and economic evidence.” It also mentioned the “interesting coincidence” surrounding the rental of the Luksic house to Mr. Trump’s relatives. Separately, a group in Minnesota opposed to the mining, Save the Boundary Waters, has called the rental arrangement “deeply troubling” and has seized on it to cast doubt on the administration’s actions.

The White House and representatives for the couple declined to answer questions about whether the rental deal had been reviewed by ethics officials. “Both Mr. Kushner and Ms. Trump follow the ethics advice they received when they entered government service,” said Peter Mirijanian, a spokesman for Mr. Kushner’s lawyer, Abbe Lowell.