The White House said Mr. Trump filed an extension for his 2017 tax return and that he will submit his complete return by mid-October.

WASHINGTON — For decades, presidents have publicly released their tax returns each year — an act of transparency and a way to connect and commiserate with Americans on Tax Day.

On Tuesday, President Trump did not even file his taxes.

White House officials said Mr. Trump, who has steadfastly refused to make any of his previous tax returns public, requested a six-month extension because of the complexity of preparing his 2017 returns. He plans to file by mid-October, officials said.

The announcement came on a day that the president and his allies used to remind people about Mr. Trump’s sweeping tax cuts that will lead to savings for many people when the next Tax Day rolls around in April 2019.

“So many people are seeing the benefits of the Tax Cut Bill,” Mr. Trump tweeted from Mar-a-Lago, his estate in Florida, where he played host to Shinzo Abe, the prime minister of Japan.

In an article published in USA Today, Mr. Trump wrote: “On this Tax Day, America is strong and roaring back. Paychecks are climbing. Tax rates are going down. Businesses are investing in our great country. And most important, the American people are winning.”

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…