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 did not require disclosure of portions of his business activities.

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 would not be held liable, the Trump Organization said. The value of his investments, however, would certainly 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.”

“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.

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.