The public disclosure of the document has now set off new questions about whether the president could potentially run afoul of a provision in the Constitution known as the Emoluments Clause, which essentially prohibits federal government officials from accepting gifts from foreign governments. The clause has become a cudgel for Mr. Trump’s critics, who argue that the presidency of a businessman raises a host of potential conflicts of interest, leading some groups to sue.

“Complying with the United States Constitution is not an optional exercise, but a requirement for serving as our nation’s president,” Mr. Cummings wrote in a letter to George Sorial, the Trump Organization’s chief compliance counsel. “If President Trump believes that identifying all of the prohibited foreign emoluments he is currently receiving would be too challenging or would harm his business ventures, his options are to divest his ownership or submit a proposal to Congress to ask for our consent.”

In a statement, a spokeswoman for the Trump Organization said: “We have received and are in the process of reviewing the letter. We take these matters seriously and are fully committed to complying with all of our legal and ethical obligations.”

Later on Wednesday, the top House Judiciary Committee Democrats sent a letter to the president himself, asking that he provide a “full accounting” of all possible foreign emoluments he had received.

One legal case over these profits is pending in Federal District Court in Manhattan, where Mr. Trump’s first formal response, being handled by the Justice Department, is due on June 9. By donating all profits paid by foreign government officials to the Trump Organization, the company could potentially eliminate vulnerability to at least part of the claim that the president and his family were benefiting financially from payments by foreign entities.