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Once again thumbing his nose at a time-honored tradition, Donald J. Trump said Friday that he does not believe voters have a right to see his tax returns, and he insisted it was “none of your business” when pressed on what tax rate he pays.

The remarks from Mr. Trump signal that he has little intention of disclosing verifiable details of his income or what fuels his wealth, a matter of endless speculation for a candidate who boasts of being a billionaire many times over despite his past brushes with bankruptcy and increasing reliance on celebrity-oriented income and licensing deals that use his name.

While not required to release their tax returns, all the major party presidential nominees have done so for roughly the past four decades, including President Richard M. Nixon, who released them despite undergoing an Internal Revenue Service audit. Mr. Trump has cited continuing I.R.S. audits of his taxes in refusing to release his returns.

When Mr. Trump was asked on ABC’s “Good Morning America” whether he thought voters had a right to see his returns, he replied, “I don’t think they do.”

Mr. Trump added of his taxes: “It’s under routine audit. When the audit ends, I’m going to present them. That should be before the election. I hope it’s before the election.”

But when asked by the interviewer, George Stephanopoulos, what effective tax rate he pays, Mr. Trump said, “It’s none of your business.” He added, “You’ll see it when I release, but I fight very hard to pay as little tax as possible.”

The release of tax returns bedeviled Republicans during the 2012 presidential election, when Mitt Romney delayed releasing his until September. His effective tax rate, which was below 20 percent, was used by President Obama’s team to lampoon him as a wealthy corporate raider who was out for himself and who could not understand how regular people lived. Mr. Trump has said that Mr. Romney erred in waiting so long to release his taxes and should have done so sooner.

For many years, Mr. Trump’s wealth has been a moving target, subject to much estimation, debate and even litigation.

Last summer, when Mr. Trump filed the personal financial disclosures required of presidential candidates, his campaign released a statement saying that he was worth more than “TEN BILLION DOLLARS,” capitalizing the outsize figure. When the 92-page document became public, the disclosures by Mr. Trump indicated that he had at least $1.4 billion in assets, including his real estate developments and golf clubs.

Fortune recently pegged his worth at $3.72 billion. Forbes calculated it at $4.5 billion, as of September 2015.

Mr. Trump disputed both numbers, just as he objected to an estimate a decade earlier when Timothy L. O’Brien, a reporter for The New York Times, wrote a book that placed the businessman’s net worth at $150 million to $250 million, based on three confidential sources. During a well-publicized episode, he sued Mr. O’Brien for defamation, but Mr. Trump ultimately failed to prove his case.

While his tax returns would not show Mr. Trump’s net worth, they would show investment income and where those investments are held, liens and the scope and type of his charitable contributions.

Kenneth A. Gross, a lawyer with Skadden who deals regularly with tax issues, suggested that the contents of Mr. Trump’s tax returns were certainly of public interest because they would provide insight into his finances that his previously disclosed financial documents do not.

“Obviously it could raise issues about deductions, reporting of income, all sorts of things that we worry about when we file our tax returns,” Mr. Gross said. “There’s obviously something of interest because it’s being audited. It would be, I think, important to see what’s in these returns before he becomes the nominee of the Republican Party.”

But Mr. Trump was adamant in his interview on Friday that “people will learn nothing” from his returns, noting how he had released his financial disclosure statement.

“I put in financials, 100 pages worth of financials, that show that I built a company that’s worth more than $10 billion,” Mr. Trump said. “It shows cash. It shows cash flows. It shows everything. You learn very little from tax returns, but nevertheless, when the audit is complete, I will release. I have no problem with it.” He added that he has no offshore accounts.

As the issue of Mr. Trump’s returns bubbled up over the past week, Democrats treaded relatively lightly on the matter, particularly since Hillary Clinton faces pressure to release transcripts of her paid speeches to Wall Street banks like Goldman Sachs. But on Wednesday Mrs. Clinton seized on Mr. Trump’s reluctance to release his returns.

“So you’ve got to ask yourself, ‘Why doesn’t he want to release them?’ ” Mrs. Clinton said on Wednesday. “Yeah, well, we’re going to find out.”

She and Bill Clinton have released their tax returns going back to 1977, when he first entered political life.

The I.R.S. will not confirm if a person is being audited or discuss their returns, but Eric Smith, a spokesman for the agency, said taxpayers are free to publicize their own financial documents at any time.

“Nothing prevents individuals from sharing their own tax information,” Mr. Smith said.

In a letter on his campaign website, Mr. Trump’s tax counsels wrote in March that his returns have been under “continuous examination” by the I.R.S. since 2002 because he has a big business. The audits from those returns from 2002 to 2008 have been completed, they wrote, but lingering questions about those returns remain, an apparent explanation as to why he will not release years no longer under “examination.”

The public interest group Common Cause put out a statement calling on Mr. Trump to release the tax returns, pointing out that he released returns from the early 2000s that were under audit to gambling commissions in New Jersey and Pennsylvania.

Mr. Trump has given different explanations for why he will not release his taxes over the years. In 2011, when he contemplated running for president, Mr. Trump said he would release his tax returns when President Obama released his birth certificate. Mr. Obama made the birth certificate public in April 2011, and Mr. Trump announced a few weeks later that he would not run for president.

Last year, Mr. Trump said he was still considering whether to release the returns, but he made no mention of the audits until this year.

Tax experts remain divided on the wisdom of Mr. Trump’s releasing his returns, with some arguing that it would be malpractice to advise a client to make such information public during an audit and others saying that he should have nothing to hide.

Robert J. Kovacev, a tax lawyer with Steptoe & Johnson who previously worked at the Department of Justice, said the scrutiny that Mr. Trump’s returns would face could add years to the audit because the I.R.S. would be pressured to examine details that critics of Mr. Trump seized upon. That could impose additional costs on Mr. Trump and disrupt his negotiations with the agency.

“If you put it out in public, it’s almost like you’re crowdsourcing the audit,” Mr. Kovacev said.

While Mr. Trump has said that he strives to pay as little tax as possible, Mr. Kovacev suggested that his returns could have information about offshore holdings or legal tax maneuvers that his accountants use that make his income appear lower or show losses.

Some tax specialists see no legitimate reason for Mr. Trump to hold back. “When you file your return with the I.R.S. or any taxation authority you are filing your returns under penalty of perjury that what you are filing is true and correct,” said Laurie B. Kazenoff, a former I.R.S. tax lawyer now with the firm Meltzer Lippe. “You should be standing by what you filed regardless of any audit.”