His initial invocation of the tax code provision — Section 6103 — was novel and set off a flurry of legal scholarship. The section gives the chairmen of Congress’s tax-writing committees unique powers to request information on any taxpayer from the I.R.S. and says only that the executive branch “shall” furnish the material upon request. The House Ways and Means Committee and Senate Finance Committee routinely use this method to study the effects of tax policy on real taxpayers, but there is scant precedent for using it to study a president’s tax information — a fact that Republicans seized on to oppose the effort.

Ultimately, Democrats decided it posed too many risks to bring directly to court.

Democrats have clamored for years for Mr. Trump to release his returns, as every other modern presidential nominee had done before him. They have speculated that the president is trying to hide details of his actual financial worth as well as information that could reveal conflicts of interest between his businesses and his governmental responsibilities. Some Democrats argue they could also reveal evidence of tax evasion.

But when Mr. Neal ultimately made his request in early April for six years of Trump personal and business returns, he said he needed the information for a narrower Ways and Means investigation of “the extent to which the I.R.S. audits and enforces the federal tax laws against a president.”

He repeated that justification on Friday.

The requests infuriated the president and his family. Mr. Trump, his personal lawyers and his Republican allies say that rationale is absurd and that Democrats are clearly concocting a fake investigation to justify getting ahold of information they can use to politically embarrass the president.

Mr. Trump’s lawyers have already formalized those arguments in two lawsuits meant to stop companies that have worked with the president from handing over financial information subpoenaed by other House committees.

But it was up to Mr. Trump’s government, not his private lawyers, to decide on the Ways and Means request. After weeks of delays, Mr. Mnuchin formally rejected the request in writing on Monday, telling Mr. Neal that after consulting Treasury and Justice Department lawyers, he had determined that the request “lacks a legitimate legislative purpose” and that he was not authorized to disclose the information in question.

“As you have recognized, the committee’s request is unprecedented, and it presents serious constitutional questions, the resolution of which may have lasting consequences for all taxpayers,” Mr. Mnuchin wrote. He added that the department would be willing to provide the committee more generalized information about how the I.R.S. conducts presidential audits.