Federal officials faced a choice about how to pass those savings on to taxpayers. One option would have been to make most people wait until they filed tax returns this spring, delivering a tax-season windfall but essentially delaying the cut by a year.

Instead, the I.R.S. chose to begin withholding less from workers’ paychecks early last year. That put more money in workers’ pockets right away, but made the effects of the tax cut harder to see, since the savings amounted to just a few dollars per pay period for many people.

The new law made numerous changes to the tax code — eliminating and capping some deductions and credits while increasing others — and the revised withholding rules did not account for every situation. As a result, government auditors warned last year that the withholding changes would reduce refunds for several million Americans.

Treasury officials acknowledged on Friday that some people had struggled to navigate the new withholding setup, leading them to underpay their taxes. The department will not charge a penalty to those who paid at least 80 percent of their total tax liability during the year, the officials said. Previously, the penalty threshold was 85 percent.

As of last week, I.R.S. statistics showed that the average refund had not changed for those who had filed. But total filings were down, and the share of returns producing a refund had declined by 0.5 percent age points, or about 300, 000 filers. (Experts caution against reading too much into tax statistics before the April filing deadline.)

“You can see people potentially being frustrated if the tax season isn’t playing out the way they expected,” said Michelle Meyer , chief United States economist for Bank of America Merrill Lynch. “Other people might be quite pleased. It is quite split how people are being impacted by the tax cut.”

Democrats have accused the Trump administration of political gamesmanship .

“The Treasury Department under-withheld taxes from millions of families’ paychecks to make the benefits of the tax law appear greater before the 2018 election, and the bill is now coming due,” Senator Ron Wyden of Oregon , the top Democrat on the Finance Committee, said in an emailed statement . “Families who depend on annual tax refunds to pay down debt, cover medical expenses and afford car repairs are discovering their refunds are smaller or they owe money. ”