During a debate in January, Mr. Trump said he would put his holdings in a blind trust, an arrangement in which a public official lets a financial manager control his wealth and does not know exactly how the money is invested. But in the next breath, he acknowledged the problem with that strategy: “Well, I don’t know if it’s a blind trust if Ivanka, Don and Eric run it.”

In an interview, Alan Garten, a lawyer for the Trump Organization, spoke of the difficulty of the task. “There has been a huge event — a historic event — that has occurred,” he said. “There is no question that makes my job more complicated.”

Under federal laws, executive branch employees must comply with conflict-of-interest rules that guard against being influenced by personal investments, and they must curb payments from sources outside the government. As a result, employees may have to recuse themselves from working on matters where they may have conflicts, holding certain properties or accepting money. For example, when Henry Paulson, the former Goldman Sachs executive, became Treasury secretary in 2006, he pledged to sell about $470 million in company stock to comply with conflict-of-interest rules.

Image Mr. Trump announced Trump University in 2005. The university is the subject of lawsuits in California and New York. Credit... Bebeto Matthews/Associated Press..

But the president and vice president were exempted from such laws, on the theory that they needed to be able to carry out their constitutional duties without restraint. So President Trump will be able to take actions pertaining to another country even if he has business interests there.

Federal laws like those against bribery and receiving benefits from foreign countries still apply to the president. Enforcement would fall to the Justice Department or to Congress, which could pursue criminal or impeachment proceedings if evidence suggests laws were broken.

Mr. Trump will be required next year to file an updated personal financial disclosure listing his holdings, similar to the forms he has filed the past couple of years as a candidate. But Mr. Trump will not be required to make public his income tax returns, which he declined to do during the campaign, citing a continuing audit by the Internal Revenue Service, an agency he will now control. If he did release them, the tax returns could provide transparency into his international business dealings and other potential conflicts that may arise.