Cheryl Mills, Clinton's top aide and chief of staff at the U.S. State Department, gave investigators access to her laptop as part of the deal, according to Utah Rep. Jason Chaffetz. In exchange, their findings couldn't be used against her, he said.
"This is beyond explanation. The FBI was handing out immunity agreements like candy. I've lost confidence in this investigation and I question the genuine effort in which it was carried out," Chaffetz said in a statement to ABC News. "Immunity deals should not be a requirement for cooperating with the FBI."
Clinton aide Heather Samuelson, who worked with Mills to sort Clinton's emails, also received a similar immunity deal.
Beth Wilkinson, the attorney for Mills and Samuelson, said in a statement to ABC News: "As the government indicated in these letters, the DOJ and FBI considered my clients to be witnesses and nothing more. Indeed, the Justice Department assured us that they believed my clients did nothing wrong. At all points my clients cooperated with the government’s investigation, including voluntarily participating in interviews with the FBI and DOJ."
According to The New York Times, two additional staffers were granted immunity for cooperating with authorities.
The Associated Press first reported the new details of the immunity agreements.
The Clinton campaign criticized Chaffetz's comments about the immunity deal and investigation, which the FBI closed without recommending charges against Clinton for using a private email server as the nation's top diplomat.
Rep. Elijah Cummings, D-Maryland, the top Democrat on the House Oversight Committee, said Mills' immunity deal was limited and did not apply to testimony provided to Congress or comments made to the FBI.
"Of course, Republicans are trying to make political hay out of this, but the facts are that Ms. Mills cooperated fully with the Justice Department and Congress, the FBI concluded that there was no basis for any criminal prosecution, and even Chairman Gowdy praised Ms. Mills for voluntarily answering every single question in his marathon, nine-hour interview with her more than a year ago," he said in a statement. "Republicans will stop at nothing to tear apart the FBI’s independent investigation to try to damage Secretary Clinton’s presidential campaign.”
FBI Director James Comey said Clinton and her aides were "extremely careless" for their handling of classified information.