Nonprofit groups that exist primarily to influence political campaigns, including so-called 527 organizations, will still be required to report the names of large donors, as will charities that accept tax-deductible contributions.

Conservative groups and donors had been lobbying the Trump administration to make the change, partly by arguing that the reporting requirement made their funders vulnerable to exposure by the I.R.S. and state regulators.

“Transparency is meant for the government, not for private individuals,” said Philip Ellender, the head lobbyist for Koch Industries, the international conglomerate owned by the Koch brothers. Koch Industries began lobbying the White House on the issue after President Trump’s election, according to lobbying filings.

Additionally, Americans for Prosperity and other 501(c)(4) organizations in the Koch brothers’ network of advocacy groups were among dozens of such nonprofit groups to sign onto a letter sent in May to Mr. Trump and Mr. Mnuchin declaring a policy change “an issue of utmost importance.” The letter accused the I.R.S. of “targeting of nonprofit organizations on the basis of ideology.”

Officials with the Treasury Department largely echoed that reasoning, explaining that the move was driven in part by the I.R.S.’s inappropriate targeting of political groups during the administrations of Presidents George W. Bush and Barack Obama. The I.R.S. inspector general found that both conservative and progressive groups were targeted and that I.R.S. officials inappropriately sought information on donors to Tea Party groups as well as to liberal groups.

In guidance issued by the I.R.S. late on Monday, administration officials said that the agency did not need personally identifiable donor information “in order for it to carry out its responsibilities.”

“The requirement to report such information increases compliance costs for some private parties, consumes I.R.S. resources in connection with the redaction of such information, and poses a risk of inadvertent disclosure of information that is not open to public inspection,” the guidance said.