The mystery around a $14 billion deal between U.S. Steel and Nippon Steel continued to deepen, as President Donald Trump said this week that the United States would have a “golden share” in the iconic American metal manufacturer, a move that would potentially give the federal government an unusually substantial amount of control over corporate decisions.

“We have a golden stock. We have a golden share, which I control, or the president controls,” Trump told reporters in the East Room of the White House on Thursday. “Now I’m a little concerned, whoever the President might be, but that gives you total control.”

The comments, which echo those made last month by a Republican Senator in U.S. Steel’s home state of Pennsylvania, suggest that Mr. Trump is insisting on having expansive influence over the steel company as a condition for allowing the deal to close.

Yet details of how a “golden share” would work remain murky, as U.S. Steel and Nippon Steel scramble to finalize their deal, which Mr. Trump announced in a surprise social media post last month.

Neither Mr. Trump, nor the companies, have confirmed whether the deal is a takeover of U.S. Steel by Nippon, a partnership between the two companies or some new form of government-backed venture.

Last week, the powerful United Steelworkers union, which had long opposed a sale to Nippon, sent an information request to U.S. Steel, pushing for more information about the deal.