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Speaker John BoehnerJohn BoehnerLobbyists bounce back under Trump Business groups silent on Trump's Ex-Im nominee Chaffetz won't run for reelection MORE (R-Ohio) on Tuesday called on Hillary ClintonHillary Rodham ClintonPoll: 85 percent of Clinton supporters would vote for her again OMB director: Government shutdown not a 'desired end' Poll: Almost half say Trump off to poor start MORE to turn over her private email server to a "neutral third party" to determine what should be released to the public.

"The American people deserve all the facts about what happened in Benghazi. That's why it's so important for Secretary of State Hillary Clinton to turn over her personal server to a neutral third party," BoehnerJohn BoehnerLobbyists bounce back under Trump Business groups silent on Trump's Ex-Im nominee Chaffetz won't run for reelection MORE said at a news conference.

"I think that is the fairest way to make sure that we have all the documents that belong to the public, and ultimately all the facts."

Clinton, who is expected to launch her presidential campaign soon, has come under fire in recent weeks, after it was revealed she had used a private email account to conduct official business when she was leading the State Department.

Clinton defenders quickly accused Boehner of using the email controversy to score points with conservatives and play politics with a national tragedy.

"Hillary Clinton took full responsibility, immediate action, and was fully transparent in making sure the tragedy that occurred in Benghazi will not be repeated," said Adrienne Watson, a spokeswoman for Correct the Record, which is funded by the Democratic-aligned PAC American Bridge 21st Century. 

"Republican politicians remain relentlessly focused on shamefully using the Benghazi tragedy for political benefit and they are taking their eye off the ball on creating jobs and growing our economy," she said.

Rep. Trey GowdyTrey GowdyFive questions for the House's new Russia investigator Chaffetz decision stuns Washington Who will replace Chaffetz on Oversight? MORE (R-S.C.), chairman of the House select committee investigating the Benghazi attack, has given Clinton two weeks to submit any emails to his committee related to the assault that killed four Americans.

And new House Oversight Committee Chairman Jason ChaffetzJason ChaffetzHow Chaffetz could get rich on K Street Oversight asks Trump for details on foreign profit donations Jason Chaffetz exploring private sector jobs: report MORE (R-Utah) said his panel would seek access to Clinton emails from the private server.

Boehner pushed back on the suggestion that the GOP is on a "witch hunt."

"The way forward is for the secretary to turn over all of her emails that pertain to the public," the Speaker said. "But some neutral third party is gonna have to make some decisions about which documents are personal and which ones are public record.

"And so far she's been unwilling to do this."

— Updated at 12:42 p.m.