That cheerful message on Tuesday was undercut by a systemwide crash of the Internal Revenue Service computers, which prevented taxpayers and preparers from filing returns online.
Many people file for more time to prepare their returns; I.R.S. officials said they expected as many as 15 million to do so this year. But the president’s decision to seek an extension broke with years of tradition established by his predecessors and once again underscored the fact that Mr. Trump’s tax returns remain a state secret.
Previous presidents have routinely filed their tax returns on time and released them publicly while running for office and once they assumed the presidency, in part to show how much they earned and how much they donated to charity.
President Barack Obama’s returns showed that he earned millions of dollars as he entered the White House in 2009, almost all of it from royalties related to Mr. Obama’s books, “Dreams From My Father” and “The Audacity of Hope.” Sales of those books made him a multimillionaire.
But Mr. Obama’s returns, which were posted on the White House website each year in April, revealed that his income plummeted after that as sales of the books began to slow. In 2012, Mr. Obama made $608,000, with most of his income coming from his presidential salary of $400,000 a year.
That year, Mr. Obama and his wife, Michelle, gave $150,000 of their income, or about 25 percent, to charity.
Richard M. Nixon was the first modern president to make his tax returns public. He did so under pressure, after being accused of having improperly taken a huge tax deduction — eliminated by Congress — for donating his presidential papers.
In 1973, Jack White, a reporter for The Providence Journal-Bulletin, broke the news that Nixon had paid just $878.03 in 1971 even though he had income of more than $400,000. The article led to Nixon’s famous quotation: “People have got to know whether or not their president is a crook. Well, I am not a crook.”
Not long after, the I.R.S. announced it would audit the president’s returns, and Nixon released five years’ worth of tax documents. Presidents have largely done so ever since.
Until Mr. Trump.
His tax returns have long been a source of speculation and criticism. Mr. Trump has said in the past that, as a businessman, he fought to pay as little tax as possible so that the government would not waste his money.
But he has insisted that he was advised not to reveal his tax returns as long as they were subject to a continuing I.R.S. audit, a claim that critics have derided as little more than a convenient excuse.
All presidential tax returns are automatically audited, making it increasingly unlikely that Mr. Trump will willingly release his returns while in office.
Although portions of Mr. Trump’s returns have leaked in the past, they remain one of the most closely guarded secrets in Washington. Last year, the departing commissioner of the I.R.S., John A. Koskinen, said that the agency was building a new vault to protect hard copies of the returns.
Given the president’s longstanding refusals, there was little expectation that Mr. Trump would make his 2017 tax returns public. But the decision to seek a six-month extension came as something of a surprise.
Mr. Trump filed last year for a similar extension of his 2016 taxes as he and his accountants faced the task of preparing a tax return for the first time as president.
But the president’s tax experts had more than a year to get ready for his 2017 returns. White House officials did not explain why Mr. Trump’s accountants would need an additional six months.