The Times story says that account is false - that, in reality, Fred Trump spent decades quietly ceding his fortune and his business empire to his son, in ways that seemed created to avoid taxes on gifts and inheritance.
Blasio has threatened the head of state penalties - both from the city and from the state of NY.
Trump's lawyer, Charles Harder said the report was "100% false" in a statement Tuesday.
In New York, tax officials had already been looking into whether Trump or his charitable foundation misrepresented their tax liability.
After reviewing the Times article, Fred Slater, a CPA who has advised real estate professionals for more than 40 years, said he estimates Trump and his siblings could owe NY state more than $400 million in unpaid taxes, interest and penalties.
On Capitol Hill, some Democrats renewed calls for Trump to release his tax returns - which he has repeatedly declined to do, unlike his predecessors. That should have produced a tax bill of at least $550 million, based on a 55 per cent tax on gifts and inheritance at the time. By the time Trump had graduated from college, the report says, he was getting the equivalent of $1 million a year from his father.
The Times story, which was published online on Tuesday afternoon, reported that Trump had participated in "dubious tax schemes" that allowed his father to pass him more than US$413 million (NZ$631m) while minimising tax payments.
Johnston said The Times' story "establishes beyond a doubt that Donald Trump has been involved in years, decades, of criminal tax evasion". Earlier this year, former Forbes reporter Jonathan Greenberg released the recording of a 1984 phone call made to him by someone who sounds eerily similar to Donald Trump. "The facts upon which the Times bases its false allegations are extremely inaccurate".
What we learned from Chicago police officer Jason Van Dyke's testimony
When asked what he did next, Van Dyke responded, "I shot him". "His eyes are still bugged out, his face, no expression in it". He said he lowered his weapon, reassessed and continued firing "on my approach". "I yelled, 'Drop the knife'".
An attorney for President Trump has denied any wrongdoing. Orrin Hatch, R-Utah, said he'd be "happy to look into the president's returns, though "right now, I don't know enough about it". His father went on to say that everything he touched turned to gold".
The assertion was pounced on by several late-night talk show hosts, including comedian Stephen Colbert, the host of The Late Show on CBS.
During his campaign for office, then-candidate Trump broke with presidential election norms when he refused to produce his tax returns for public review.
The mayor of NY bill de Blasio in connection with the material of the NYT about a possible multi-year evasion of U.S. President Donald trump from paying taxes, said that he would try to recover all those payments to the budget, which he underpaid the city and the state.
It said that, starting in the 1990s, Donald Trump had helped his father lower his tax bills via a sham corporation that processed padded invoices, by using improper tax deductions and by systematically undervaluing his father's real estate properties.
FILE - Eric Trump, left, and Donald Trump Jr., executive vice presidents of The Trump Organization, pose for a photograph at an event for Scion Hotels, a division of Trump hotels, June 5, 2017, in NY.
It marked the first time a court interpreted anti-corruption clauses in the constitution, known as emoluments clauses, and applied them to a sitting president.