On the campaign trail, Donald J. Trump, the Republican presidential nominee, has sold himself as a businessman who has made billions of dollars and is beholden to no one.

But an investigation by The New York Times into the financial maze of Mr. Trump’s real estate holdings in the United States reveals that companies he owns have at least $650 million in debt — twice the amount than can be gleaned from public filings he has made as part of his bid for the White House. The Times’s inquiry also found that Mr. Trump’s fortunes depend deeply on a wide array of financial backers, including one he has cited in attacks during his campaign.

For example, an office building on Avenue of the Americas in Manhattan, of which Mr. Trump is part owner, carries a $950 million loan. Among the lenders: the Bank of China, one of the largest banks in a country that Mr. Trump has railed against as an economic foe of the United States, and Goldman Sachs, a financial institution he has said controls Hillary Clinton, the Democratic nominee, after it paid her $675,000 in speaking fees.

Real estate projects often involve complex ownership and mortgage structures. And given Mr. Trump’s long real estate career in the United States and abroad, as well as his claim that his personal wealth exceeds $10 billion, it is safe to say that no previous major party presidential nominee has had finances nearly as complicated.

As president, Mr. Trump would have substantial sway over monetary and tax policy, as well as the power to make appointments that would directly affect his own financial empire. He would also wield influence over legislative issues that could have a significant impact on his net worth, and would have official dealings with countries in which he has business interests.

Yet The Times’s examination underscored how much of Mr. Trump’s business remains shrouded in mystery. He has declined to disclose his tax returns or allow an independent valuation of his assets.

Earlier in the campaign, Mr. Trump submitted a 104-page federal financial disclosure form. It said his businesses owed at least $315 million to a relatively small group of lenders and listed ties to more than 500 limited liability companies. Though he answered the questions, the form appears to have been designed for candidates with simpler finances than his, and portions of his activities were not disclosed.

Beyond finding that companies owned by Mr. Trump had debts of at least $650 million, The Times discovered that a substantial portion of his wealth is tied up in three passive partnerships that owe an additional $2 billion to a string of lenders, including those that hold the loan on the Avenue of the Americas building. If those loans were to go into default, Mr. Trump might not be held personally liable, but the value of his investments would sink.

Mr. Trump has said that if he were elected president, his children would be likely to run his company. Many presidents, to avoid any appearance of a conflict, have placed their holdings in blind trusts, which typically involves selling the original asset, and replacing it with different assets unknown to the seller.

Mr. Trump’s children seem unlikely to pursue that option.

Richard W. Painter, a professor of law at the University of Minnesota and, from 2005 to 2007, the chief White House ethics lawyer under President George W. Bush, compared Mr. Trump to Henry M. Paulson Jr., a former chief executive of Goldman Sachs whom Mr. Bush appointed as Treasury secretary.

Professor Painter advised Mr. Paulson on his decision to sell his Goldman Sachs shares, saying it was clear that Mr. Paulson could not simply have placed that stock in trust and pretended it did not exist.

If Mr. Trump were to use a blind trust, the professor said, it would be “like putting a gold watch in a box and pretending you don’t know it is in there.”

‘We Overdisclosed’

“I am the king of debt,” Mr. Trump once said on CNN. “I love debt.” But in his career, debt has sometimes gotten the better of him, leading to at least four business bankruptcies.

He is, however, quick to stress that these days his companies have very little debt.

Mr. Trump indicated in the financial disclosure form he filed in connection with this campaign that he was worth at least $1.5 billion, and has said publicly that the figure is actually greater than $10 billion. Recent estimates by Forbes and Fortune magazines and Bloomberg have put his worth at less than $5 billion.

To gain a better understanding of Mr. Trump’s holdings and debt, The Times engaged RedVision Systems, a national property information firm, to search publicly available data on more than 30 properties in the United States. The Times identified these assets through Federal Election Commission filings, information provided by the Trump Organization and records, such as filings with the Securities and Exchange Commission.

The search covered thousands of pages of public information, including loan documents, land leases and property deeds. It concentrated on Mr. Trump’s commercial holdings, including office towers, golf courses, a vineyard in Virginia and even an industrial building in South Carolina that he ended up with after a troubled business venture involving Donald Trump Jr. The inquiry also examined some of Mr. Trump’s residential properties, including his penthouse apartment on Fifth Avenue and a house he owns in Beverly Hills, Calif. The examination did not include Mr. Trump’s dealings outside the United States.

That Mr. Trump seems to have so much less debt on his disclosure form than what The Times found is not his fault, but rather a function of what the form asks candidates to list and how.

The form, released by the Federal Election Commission, asks that candidates list assets and debts not in precise numbers, but in ranges that top out at $50 million — appropriate for most candidates, but not for Mr. Trump. Through its examination, The Times was able to discern the amount of debt taken out on each property, and its ownership structure.

At 40 Wall Street in Manhattan, a limited liability company, or L.L.C., controlled by Mr. Trump holds the ground lease — the lease for the land on which the building stands. In 2015, Mr. Trump borrowed $160 million from Ladder Capital, a small New York firm, using that long-term lease as collateral. On his financial disclosure form that debt is listed as valued at more than $50 million.

Allen Weisselberg, chief financial officer of the Trump Organization, said that Mr. Trump could have left the liability section on the form blank, because federal law requires that presidential candidates disclose personal liabilities, not corporate debt. Mr. Trump, he said, has no personal debt.

“We overdisclosed,” Mr. Weisselberg said, explaining that it was decided that when a Trump company owned 100 percent of a property, all of the associated debt would be disclosed, something that he said went beyond what the law required.

Filing Taken at ‘Face Value’

For properties where a Trump company owned less than 100 percent of a building, Mr. Weisselberg said, those debts were not disclosed.

Mr. Trump, for example, has a 50 percent stake in the Trump International Hotel Las Vegas. In 2010, the company that owns the hotel refinanced a $190 million loan, according to Real Capital Analytics, a commercial real estate data and analytics firm.

Mr. Weisselberg said that a Trump entity was responsible for half the debt, and that all but $6.4 million of the loan had been paid off.

The Times found three other instances in which Mr. Trump had an ownership interest in a building but did not disclose the debt associated with it. In all three cases, Mr. Trump had passive investments in limited liability companies that had borrowed significant amounts of money.

One of these investments involves an office tower at 1290 Avenue of Americas, near Rockefeller Center. In a typically complex deal, loan documents show that four lenders — German American Capital, a subsidiary of Deutsche Bank; UBS Real Estate Securities; Goldman Sachs Mortgage Company; and Bank of China — agreed in November 2012 to lend $950 million to the three companies that own the building. Those companies, obscurely named HWA 1290 III LLC, HWA 1290 IV LLC and HWA 1290 V LLC, are owned by three other companies in which Mr. Trump has stakes.

Ultimately, through his investments, Mr. Trump is a 30 percent owner of the building, records show. Vornado Realty Trust owns the other 70 percent and is the controlling partner.

A similar ownership structure is in place at 555 California Street in San Francisco, formerly the Bank of America Center. There, Pacific Life Insurance Company and Metropolitan Life Insurance Company lent $600 million in 2011 to a limited liability company of which Vornado owns 70 percent and Mr. Trump owns 30 percent.

Green Street Advisors, a real estate research firm, estimates the combined value of the two buildings to be about $3.7 billion.

On a smaller scale, Mr. Trump also has a 4 percent partnership interest in a company that has an interest in a large Brooklyn housing complex, and owes roughly $410 million to Wells Fargo, according to Bloomberg data.

The full terms of Mr. Trump’s limited partnerships are not known. The current value of the loans connected to them is roughly $1.95 billion, according to various public documents.

Mr. Weisselberg, the Trump Organization’s chief financial officer, said that neither Mr. Trump nor the company were responsible for the debt associated with the limited partnerships.

Still, as with all of the properties in which Mr. Trump holds an interest, the value of the buildings as well as the terms and magnitude of their debt could have a major impact on his personal fortune.

Mr. Trump, Mr. Weisselberg added, was liable for a “small percentage of the corporate debt” listed on the federal filing but would not elaborate.

Other instances in which Mr. Trump could be personally responsible can be found in public filings. He guaranteed as much as $26 million for the loan taken out against his land lease at 40 Wall Street, money the lender could take if certain things went wrong.

The United States Office of Government Ethics, which reviewed Mr. Trump’s financial filing before the F.E.C. released it, said it does not comment on submissions by individual candidates.

The agency’s procedures for staff members reviewing presidential submissions, a copy of which was obtained by The Times through a Freedom of Information Act request, say the Office of Government Ethics does not audit reports for accuracy.

“Disclosures are to be taken at ‘face value’ as correct, unless there is a patent omission or ambiguity or the official has independent knowledge of matters outside the report,” the procedures say.

Opaque Web of Investments

Tracing the ownership of many of Mr. Trump’s buildings can be a complicated task. Sometimes he owns a building and the land underneath it; sometimes, he holds a partial interest or just the commercial portion of a property.

And in some cases, the identities of his business partners are obscured behind limited liability companies — raising the prospect of a president with unknown business ties.

At 40 Wall Street, Mr. Trump does not own even a sliver of the actual land; his long-term ground lease gives him the right to improve and manage the building. The land is owned by two limited liability companies; Mr. Trump pays the two entities a total of $1.6 million a year for the ground lease, according to documents filed with the S.E.C.

The majority owner, 40 Wall Street Holdings Corporation, owns 80 percent of the land; New Scandic Wall Limited Partnership owns the rest, according to public documents. New Scandic Wall Limited Partnership’s chief executive is Joachim Ferdinand von Grumme-Douglas, a businessman based in Europe, according to these documents.

The people behind 40 Wall Street Holdings are harder to identify. For years, Germany’s Hinneberg family, which made its fortune in the shipping industry, controlled the property through a company called 40 Wall Limited Partnership. In late 2014, their interest in the land was transferred to a new company, 40 Wall Street Holdings. The Times was not able to identify the owner or owners of this company, and the Trump Organization declined to comment.

Mr. Trump has long-term ground leases on several other properties, including a golf course in New York’s Hudson Valley and retail space in Midtown Manhattan. Private owners are also behind these leases, their identities sometimes obscured by L.L.C.s.

Mr. Trump’s status in these situations is indicated by the word tenant, which is listed under his signature on many of the relevant documents.

Mr. Trump also holds a ground lease on the almost-completed Trump International Hotel in the Old Post Office building in Washington, a few blocks from the White House. The federal government, which owns the land, gave a 60-year lease to Trump Old Post Office, a limited liability company controlled by Mr. Trump and members of his family. In return, the government receives a minimum of $3 million a year from the company.

Mr. Weisselberg said that despite his holdings, Mr. Trump should not be held to the same standards that might apply to the heads of companies in highly regulated industries.

“If you take away all the fancy stuff and so on and so forth, and the five-star ratings, you are basically down to a closely held family-run business that is fundamentally different from IBM or Exxon,” Mr. Weisselberg said, quoting from an email he had received from Donald F. McGahn, a lawyer and former chairman of the F.E.C. who advised Mr. Trump on his federal filing. Mr. McGahn did not return calls for comment.

Others disagree. Mr. Trump’s opaque portfolio of business ties make him potentially vulnerable to the demands of banks, and to business people in the United States and abroad, said Professor Painter, the former chief White House ethics lawyer.

“The success of his empire depends on an ability to get credit, to get loans extended to his business entities,” he said. “And we simply don’t know a lot about his financial dealings, here or around the world.”