Further complicating matters are Mr. Trump’s decision to name his children to his transition team, and what is likely to be their informal advisory role in his administration. His daughter Ivanka Trump joined an official transition meeting on Thursday, the day before Gov. Chris Christie of New Jersey was removed from his post leading the effort.

Mr. Trump has said he will eliminate ethical concerns by turning the management of his company over to his children, an arrangement he has referred to as a blind trust.

But ethics lawyers — both Republicans and Democrats — say it is far from blind because he would have knowledge of the assets in the trust and be in contact with the people running it, making it unlike a conventional blind trust controlled entirely by an independent party.

“To say that his children running his businesses is the equivalent of a blind trust — there is simply no credibility in that claim,” said Matthew T. Sanderson, a Washington lawyer and Republican who has worked on the presidential campaigns of John McCain, Rand Paul and Rick Perry. “Yes, the American public elected him knowing he has these assets, but unless he deals with this properly there will just be a steady trickle of these conflict-of-interest stories, and it could be a drag on his presidency.”

Mr. Trump, as part of his bid for the White House, released information about his financial holdings, which include more than a dozen hotels and golf courses; commercial real estate space, including Trump Tower and 40 Wall Street in New York; and marketing deals in the United States and abroad. But it is unclear how much information was not disclosed, in part because he declined to release even a summary of his tax returns — becoming the first presidential candidate not to do so in 40 years.

Rudolph W. Giuliani, a close adviser to Mr. Trump, said on CNN’s “State of the Union” on Sunday that excluding Mr. Trump’s family from a role in his businesses “would basically put his children out of work.” The public, Mr. Giuliani said, needs to trust Mr. Trump.

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“You have to have some confidence in the integrity of the president,” Mr. Giuliani said. “The man is an enormously wealthy man. I don’t think there’s any real fear or suspicion that he’s seeking to enrich himself by being president. If he wanted to enrich himself, he wouldn’t have run for president.”

Hope Hicks, a spokeswoman for the transition, declined to respond to questions about possible conflicts of interest Mr. Trump might face as president. “The Trump Organization will respond accordingly,” she said.

A spokeswoman for Mr. Trump’s company said in a statement that the Trump Organization was already working to address possible conflicts.

“We are in the process of vetting various structures with the goal of the immediate transfer of management of the Trump Organization and its portfolio of businesses to Donald Jr., Ivanka and Eric Trump along with a team of highly skilled executives,” the statement said. “This is a top priority at the organization, and the structure that is ultimately selected will comply with all applicable rules and regulations.”

Previous presidents have encountered questions about their financial holdings. Lyndon B. Johnson, through his wife, continued to have ownership of television stations while he was president. George Washington enlisted the Treasury Department to help find a runaway slave. But presidents have often taken steps to prevent ethical questions. George Bush put his stock holdings into a blind trust after he was elected vice president, and Jimmy Carter turned his peanut farm over to a blind trust after he was elected.

As president, Mr. Trump will be exempt from a federal ethics rule that prohibits government employees and members of Congress from taking actions that could benefit their financial interests.

But the president still must comply with a law that requires annual financial disclosures of his assets. The first will not be due until May 2018, although President Obama filed one voluntarily during his first year in office.

Experts said that even if Mr. Trump was exempt from some federal ethics rules, the public will expect him to not use his office to benefit his personal finances.

“He has campaigned on a platform of getting rid of corruption and that Washington is broken and we need new, refreshing change,” said Karen Hobert Flynn, president of Common Cause, a nonprofit that pushes for accountability in government. “As president, the American public expects that Mr. Trump will be held to a higher standard.”

In a statement on Monday, the General Services Administration said that the agency realized it must examine its Old Post Office lease with Mr. Trump’s family-owned business “to allow a path to be put in place to identify and address any potential conflict of interest.”

Also on Monday, Representative Elijah E. Cummings, Democrat of Maryland and the ranking member of the Committee on Oversight and Government Reform, called for an inquiry into how Mr. Trump will handle these potential conflicts.

“The American people have the right to know — they ought to know — exactly whether decisions are possibly being made that would benefit him, his family and his associates directly,” Mr. Cummings said in an interview.

The labor dispute in Nevada represents another potential complication. The president appoints all five members of the National Labor Relations Board. But over the past year, the Trump International Hotel Las Vegas has been in a battle with the culinary workers union, at first challenging an effort by hotel employees to unionize. The labor board ruled against him in July. Then the hotel, which Mr. Trump co-owns, refused to begin negotiations with the new union, and the labor board again ruled against it, in November. Other labor disputes with employees are pending.

“Will he as president of the United States of America use the power he has to interfere — given that he has a financial interest in the outcome of these matters?” said Bethany Khan, a spokeswoman for the 57,000-member Culinary Workers Union Local 226 of Nevada.

Perhaps most troubling for Mr. Trump, several ethics lawyers said, is a relatively obscure provision of the Constitution, called the Emoluments Clause, which prohibits any government official from taking payments or gifts from a foreign government, or even from sharing in profits in a company that has financial ties to a foreign government.

Mr. Trump has had business deals with foreign governments or individuals with apparent ties to foreign governments, including multimillion-dollar real estate arrangements in Azerbaijan and Uruguay. His children have frequently traveled abroad to promote the Trump brand, making trips to Canada, the United Arab Emirates and Scotland. Closer to home, the Bank of China is a tenant in Trump Tower and is a lender for another building in Midtown Manhattan where Mr. Trump has a significant partnership interest.

“Doing business with a foreign corporation, be it in Azerbaijan, Turkey or Russia, if is it owned in part or controlled by a foreign government — any benefit that would accrue to Mr. Trump could well be a violation of the Emoluments Clause of the United States Constitution,” said Kenneth A. Gross, a political ethics and compliance lawyer in Washington.

There are also more general issues that could prove troubling. For instance, Mr. Trump will nominate the Treasury secretary, yet he owes hundreds of millions of dollars to banks, and he benefits from low interest rates set by the Federal Reserve, an institution he has criticized as political. The head of the Internal Revenue Service is also appointed by the president, and the agency is currently auditing Mr. Trump’s taxes and sets tax policy that directly affects his businesses.

But it is Mr. Trump’s real estate and financial holdings that represent the most sensitive ethical areas, the ethics lawyer said.

Mr. Trump’s children are already deeply involved in the daily operations of the Trump Organization. Ivanka is executive vice president for development and acquisitions, and is in charge of domestic and global expansion of the company’s real estate interests. Ms. Trump also has her own clothing, jewelry and footwear lines.

Even this week, Ms. Trump turned her appearance on Sunday on “60 Minutes” — with her father — into a marketing opportunity for her line of jewelry, with one of her employees urging reporters to write about the $10,800 gold bangle bracelet she wore during the interview.

Donald Jr. is also an executive vice president in the Trump Organization, and the company’s website says he directs new project acquisition and development in regions “from Eastern Europe to Southeast Asia, the Middle East to South America, mainland China to the United States.”

Eric is in charge of the Trump Organization’s golf course collection.

“We’ll be in New York and we’ll take care of the business,” Eric Trump said in an interview with “60 Minutes” that was broadcast on Sunday. “I think we’re going to have a lot of fun doing it. And we’re going to make him very proud.”