Rusal has been struggling to operate with the American sanctions in place and has appealed to the Treasury Department for relief. The United States has said it will consider lifting the ban if Mr. Deripaska cedes control of the company, and Rusal has begun the process for that to occur. In an interview with Reuters last month, the Treasury secretary, Steven Mnuchin, said he was open to easing the sanctions on Rusal, which the company has said pose a threat to its operations. “Our objective is not to put Rusal out of business,” he said.

Despite the cloud of sanctions, Rusal filed more than 100 requests for exclusions that would allow it to import aluminum products from its Russian parent company to produce furniture, portable ladders and other goods. An American aluminum titan, Century Aluminum, filed objections to all but a few of those requests.

Rusal’s first 19 requests were denied by Commerce Department officials. In late July, its 20th request was granted. To date, Commerce Department officials say they have never approved a request that another company objected to properly.

Democrats in Congress who noticed the exclusion were prepared to protest what they called suspicious timing, given that the exemption coincided with Mr. Trump’s summit meeting with Mr. Putin in Finland.

Commerce Department officials dismissed that criticism last week, saying they had coordinated with the Treasury Department unit that oversees sanctions in considering the Rusal application. The officials said that unit, the Office of Foreign Assets Control, was ultimately the decider on whether sanctions should prevent approval of an exclusion.

Treasury officials, however, denied that they had played a role in the exclusion request.

The Commerce Department “implements authorities that are separate and distinct from sanctions implemented by Treasury’s O.F.A.C.,” a Treasury spokesman said in an email. “This was a Commerce Department decision, and we were not specifically consulted.”

The Commerce Department said that the approval review lasted 12 weeks, and that “there were no objections posted by American companies for the approved request” during the monthlong comment period.