Hillary Clinton was waiting for this one on Monday night: a line of questioning about Donald J. Trump’s refusal to release his income tax returns.

And she pounced, listing off theories of why Mr. Trump would not do so.

Perhaps he did not want to reveal foreign business interests. Maybe he had not been so charitable or was not as wealthy as he claimed. But it was another possibility – that Mr. Trump had not been paying income taxes — that set off a curious response from him that sounded a lot like an admission.

“That makes me smart,” Mr. Trump said when Mrs. Clinton brought up how he had paid no taxes more than two decades ago.

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When she suggested a short time later that Mr. Trump was still paying no federal taxes and had not done so for many years, Mr. Trump offered another retort: “It would be squandered, too, believe me.”

For someone as wealthy as Mr. Trump to pay no federal income taxes would be remarkable, all the more so given the doctrine of progressive taxation long embraced by the United States.

Even before Monday’s debate, it was known that Mr. Trump had not paid any income taxes in certain years, based on paperwork he filed with New Jersey casino regulators and other instances in which his taxes appeared in a public record. But those records are all at least 25 years old.

Tax experts say that real estate developers like Mr. Trump have access to a range of tax breaks, meaning it would be possible for him to pay minimal taxes even as his wealth expanded. Others have suggested that major losses in his businesses in the 1990s may have sheltered him from paying taxes for years. A business loss in one year can be used to offset income in future years, reducing or even eliminating someone’s tax burden.

When Mitt Romney was the Republican nominee in 2012, his return from the year before revealed his effective tax rate had been 14 percent, strikingly low for someone of his wealth. He had legally benefited from the lower tax rate on so-called carried interest, which Democrats in Congress have tried unsuccessfully to reverse. Mr. Romney has been among those calling on Mr. Trump to release his taxes.

Mrs. Clinton and her husband, former President Bill Clinton, have released their 2015 returns, showing that they paid $3.6 million in federal taxes on adjusted gross income of $10.6 million, for a 35 percent tax rate. The Clintons have released taxes dating to 2007 for this campaign, in addition to taxes that they have made public during earlier campaigns.

Those disclosures have allowed Mrs. Clinton to seize on the issue to draw a contrast with Mr. Trump at the debate. She said that if Mr. Trump had not paid taxes, that meant “zero for troops, zero for vets, zero for schools or health.”

“For 40 years, everyone running for president has released their tax returns,” she said. “You can go and see nearly, I think, 39, 40 years of our tax returns — but everyone has done it.”

During the debate, the Democrat National Committee noted Mr. Trump’s statements, sending out a response: “Trump Sniffs at Paying Taxes.”

Mr. Trump says he is not releasing his tax returns because they are under a routine audit from the Internal Revenue Service, but I.R.S. officials have said he is under no obligation to keep his forms secret.

In the “spin room” after the debate, Mr. Trump disputed any suggestion that he had admitted to not paying income taxes. “No I didn’t say that at all,” he said. “I mean, if they say I didn’t, I mean, it doesn’t matter. I will say this: I hate the way our government spends our taxes.”

Mr. Trump also asserted, “Of course I pay federal taxes.”

As the questioning wore on at the debate, Mr. Trump suggested that he would disregard his lawyers’ advice and release his taxes if Mrs. Clinton released emails from her private server that have not yet been made public. A spokesman for Mr. Trump’s campaign did not immediately respond to requests for comment.

Presidential candidates are not required to make their taxes public, but doing so is seen as valuable – particularly for a candidate running on a business record — because the returns can offer insights into financial dealings, investments, charitable donations and tax payments. Mr. Trump has filed the required personal financial disclosure, which includes details of business interests – and during Monday’s debate, he suggested that viewers seek out that document for information on his finances.

“As far as my tax returns, you don’t learn that much from tax returns,” he said.

With the race in its final phase, there is substantial interest among voters in Mr. Trump making his taxes public, according to recent polls. A CBS News/New York Times Poll this month showed that 59 percent of respondents said it was necessary for him to release his tax returns. In a survey by Fox News last month, 60 percent said they believed that Mr. Trump was hiding something in his returns.

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