Donald J. Trump declared a $916 million loss on his 1995 income tax returns, a tax deduction so substantial it could have allowed him to legally avoid paying any federal income taxes for up to 18 years, records obtained by The New York Times show.

The 1995 tax records, never before disclosed, reveal the extraordinary tax benefits that Mr. Trump, the Republican presidential nominee, derived from the financial wreckage he left behind in the early 1990s through mismanagement of three Atlantic City casinos, his ill-fated foray into the airline business and his ill-timed purchase of the Plaza Hotel in Manhattan.

Tax experts hired by The Times to analyze Mr. Trump’s 1995 records said tax rules that are especially advantageous to wealthy filers would have allowed Mr. Trump to use his $916 million loss to cancel out an equivalent amount of taxable income over an 18-year period.

Although Mr. Trump’s taxable income in subsequent years is as yet unknown, a $916 million loss in 1995 would have been large enough to wipe out more than $50 million a year in taxable income over 18 years.

The $916 million loss certainly could have eliminated any federal income taxes Mr. Trump otherwise would have owed on the $50,000 to $100,000 he was paid for each episode of “The Apprentice,” or the roughly $45 million he was paid between 1995 and 2009 when he was chairman or chief executive of the publicly traded company he created to assume ownership of his troubled Atlantic City casinos. Ordinary investors in the new company, meanwhile, saw the value of their shares plunge to 17 cents from $35.50, while scores of contractors went unpaid for work on Mr. Trump’s casinos and casino bondholders received pennies on the dollar.

“He has a vast benefit from his destruction” in the early 1990s, said one of the experts, Joel Rosenfeld, an assistant professor at New York University’s Schack Institute of Real Estate. Mr. Rosenfeld offered this description of what he would advise a client who came to him with a tax return like Mr. Trump’s: “Do you realize you can create $916 million in income without paying a nickel in taxes?”

Mr. Trump declined to comment on the documents. Instead, the campaign released a statement that neither challenged nor confirmed the $916 million loss.

“Mr. Trump is a highly-skilled businessman who has a fiduciary responsibility to his business, his family and his employees to pay no more tax than legally required,” the statement said. “That being said, Mr. Trump has paid hundreds of millions of dollars in property taxes, sales and excise taxes, real estate taxes, city taxes, state taxes, employee taxes and federal taxes.”

The statement continued: “Mr. Trump knows the tax code far better than anyone who has ever run for President and he is the only one that knows how to fix it.”

In response to a Times article revealing pages of his 1995 income tax records, Mr. Trump said, “The only news here is that the more than 20 year-old alleged tax document was illegally obtained.”

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Separately, a lawyer for Mr. Trump, Marc E. Kasowitz, emailed a letter to The Times arguing that publication of the records is illegal because Mr. Trump has not authorized the disclosure of any of his tax returns. Mr. Kasowitz threatened “prompt initiation of appropriate legal action.”

Mr. Trump’s refusal to make his tax returns public — breaking with decades of tradition in presidential contests — has emerged as a central issue in the campaign, with a majority of voters saying he should release them. Mr. Trump has declined to do so, and has said he is being audited by the Internal Revenue Service.

At last Monday’s presidential debate, when Hillary Clinton suggested Mr. Trump was refusing to release his tax returns so voters would not know “he’s paid nothing in federal taxes,” and when she also pointed out that Mr. Trump had once revealed to casino regulators that he had paid no federal income taxes in the late 1970s, Mr. Trump retorted: “That makes me smart.”

The tax experts consulted by The Times said nothing in the 1995 documents suggested any wrongdoing by Mr. Trump, even if the extraordinary size of the loss he declared would have probably triggered extra scrutiny from Internal Revenue Service examiners. “The I.R.S., when they see a negative $916 million, that has to pop out,” Mr. Rosenfeld said.

The documents examined by The Times represent a small fraction of the voluminous tax returns Mr. Trump would have filed in 1995.