One of Rusal’s major shareholders, SUAL Partners Limited, was founded by Mr. Blavatnik and the Russian oligarch Viktor Vekselberg. Mr. Blavatnik, a dual American-British citizen who was born in Soviet-era Ukraine, has not had sanctions placed on him. But Mr. Vekselberg, like Mr. Deripaska, came under sanctions from the Treasury Department last year and also has drawn the interest of the special counsel investigating Russian interference in the 2016 election.

The administration’s decision to delay and ultimately lift the sanctions on Mr. Deripaska’s companies sparked outrage on the part of Democrats and Russia hawks while also leading to a surge in the stock price of Rusal.

The document outlining the terms of the deal to lift the sanctions showed that SUAL will own 22.5 percent of Rusal after the restructuring of Mr. Deripaska’s holdings. The rise in Rusal’s stock price has increased the value of SUAL Partners’ holding in the company by about $800 million relative to the value last year shortly after the sanctions were announced.

In a separate letter to Mr. Mnuchin on Monday, Senator Mark Warner of Virginia, the top Democrat on the Senate Intelligence Committee, expressed concern about the influence that could be exerted on Rusal under the Treasury deal by SUAL and a Russian bank under sanctions, VTB, as well as by Mr. Deripaska, his family and entities connected to them.

On Tuesday, the Democrats who lead the House Ways and Means, Foreign Affairs, Intelligence and Financial Services Committees said in a statement that they were “considering additional legislative actions to ensure that Treasury and these companies comply with the agreement in letter and in spirit, and to prevent something like this from happening again in the future.”

And in a letter sent to Mr. Mnuchin last week, Representative Jackie Speier, Democrat of California, who sits on the House Intelligence Committee, asked if the secretary had “ever influenced deliberations on sanctions applications when they involved an entity in which you had a financial interest or with which you had a relationship.”

While Mr. Blavatnik had given mostly to Democrats through the end of 2014, his giving has escalated drastically and shifted sharply right since then. He did not donate to Mr. Trump’s campaign or the “super PACs” that supported it, but family members gave $243,000 to the Republican National Committee during the campaign. And two of Mr. Blavatnik’s companies, including his main United States-based company, Access Industries, donated $2.5 million to the super PAC supporting Republican Senate candidates in 2016, plus another $1 million in 2017, according to Federal Election Commission records.