"The privacy interests of donors is widely recognized and valued. Various public policy initiatives have rightly encouraged donations to social welfare organizations, and these efforts are threatened when private information about donors is not adequately protected," the letter states.

The new letter, from Sen. Orrin HatchOrrin HatchHow to marry housing policy and tax reform for millions of Americans Though flawed, complex Medicaid block grants have fighting chance A guide to the committees: Senate MORE (R-Utah) and other GOP senators, says that, by requesting the confidential donor names, the agency has set in motion a process that will result in the names being available for public viewing at the IRS when the investigated groups are approved to become a 501(c)(4).

"The IRS appears to be circumventing the statutory privacy protections that Congress has long provided donors," exposing the donors to "possible harassment," the Republicans said."The public release of private donor information exposes citizens to possible harassment and intimidation by those who oppose the goals of the charitable organization."

Republicans and Democrats on Capitol Hill have been clashing over 501(c)(4) and other tax-exempt groups, some of which are spending millions of dollars this year on election advertising. 

The IRS currently says that the primary purpose of 501(c)(4) groups should not be political, which has led some legal analysts to assert that those organizations should use less than 50 percent of their budget on political causes.  

Watchdogs argue groups are misusing the 501(c)(4) tax-exempt status to keep their donors secret as they spend millions on election ads. 

The Republican senators requested that the IRS provide the statutory authority to require donor names, the frequency of requests for the information, and which officials were involved in requesting and approving the "questions requesting donor names," among other issues.

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— Bernie Becker contributed to this report.