The New York Times says Donald Trump paid just $750 (£587) in federal income tax both in 2016, the year he ran for the US presidency, and in his first year in the White House.
The newspaper - which says it obtained tax records for Mr Trump and his companies over two decades - also alleges that he paid no income taxes at all in 10 of the previous 15 years.
The records reveal "chronic losses and years of tax avoidance", it says. Mr Trump called the report "fake news".
"Actually I paid tax. And you'll see that as soon as my tax returns - it's under audit, they've been under audit for a long time," he told reporters after the story was published on Sunday.
"The IRS [Internal Revenue Service] does not treat me well… they treat me very badly. You have people in the IRS - they treat me very badly," he said.
Mr Trump has faced legal challenges for refusing to share documents concerning his fortune and business.
He is the first president since the 1970s not to make his tax returns public, though this is not required by law.
The Times said information in its report was "provided by sources with legal access to it".
The report came just days before Mr Trump's first presidential debate with Democratic rival Joe Biden and weeks before the 3 November election.
What are the key claims?
The Times said it reviewed tax returns relating to President Trump and the companies owned by the Trump Organization going back to the 1990s, as well as his personal returns for 2016 and 2017.
It said the president paid just $750 in income taxes in both 2016 and 2017, while he paid no income taxes at all in 10 of the previous 15 years, "largely because he reported losing much more money than he made".
Before becoming president, Mr Trump was known as a celebrity businessman and property mogul.
But the newspaper says his reports to the IRS "portray a businessman who takes in hundreds of millions of dollars a year yet racks up chronic losses that he aggressively employs to avoid paying taxes".
In a public filing, President Trump indicated that he earned at least $434.9m in 2018. The newspaper disputes this, alleging that his tax returns show the president had instead gone into the red, with $47.4m in losses.
The Trump Organization joined the president in denying the allegations in the report.
The company's chief legal officer, Alan Garten, told the Times that "most, if not all, of the facts appear to be inaccurate".
"Over the past decade, President Trump has paid tens of millions of dollars in personal taxes to the federal government, including paying millions in personal taxes since announcing his candidacy in 2015," he said.
What else does the report say?
The newspaper also claims that "most" of Mr Trump's biggest businesses - such as his golf courses and hotels - "report losing millions, if not tens of millions, of dollars year after year".
"That equation is a key element of the alchemy of Mr Trump's finances: using the proceeds of his celebrity to purchase and prop up risky businesses, then wielding their losses to avoid taxes," it says.
It adds that the president is personally responsible for more than $300m in loans, due to be repaid in the next four years.
The newspaper also alleges that some of President Trump's businesses have received money from "lobbyists, foreign officials and others seeking face time, access or favour" from the president.