Rep. Trey GowdyTrey GowdyGowdy: Sarah Sanders doesn't get say whether Comey broke the law Trump condemns Rice's unmasking: 'What she did was wrong' Sessions, Coats push for permanent renewal of controversial surveillance law MORE (R-S.C.), the chairman of the House Select Committee Benghazi, wants White House advisers Susan Rice and Ben Rhodes, in addition to Hillary ClintonHillary Diane Rodham ClintonBiden slams Trump over golf gif hitting Clinton Overnight Cybersecurity: Equifax hit by earlier hack | What to know about Kaspersky controversy | Officials review EU-US privacy pact Overnight Tech: Equifax hit by earlier undisclosed hack | Facebook takes heat over Russian ads | Alt-right Twitter rival may lose domain MORE, to testify, setting up high-profile confrontations. 

Gowdy said after a hearing of the committee on Wednesday that he wants Clinton, who was secretary of State during the 2012 attacks that killed four Americans, to testify. 

"I don't see how you can have any definitive accounting of Benghazi without talking to the secretary of State at the time," he added on Fox News Wednesday night. 

He also said that the appearance would not be until after January, setting up the possibility of Clinton being called to testify in the middle of her presidential campaign. 

"I need the remainder of the document production from the State Department before I can interview Secretary Clinton," Gowdy said. "They've been cooperative, and they've been helpful. But as you know, as a really good lawyer, you can't examine anyone until you have all the documents."

But there are also current White House officials Gowdy wants to testify. 

"Susan Rice has to be called," Gowdy said. "She's never been called before a committee of Congress to explain what role she played in the drafting or the giving of the White House talking points."

Rice, the national security adviser, has faced criticism for her Sunday show appearances after the attacks during which she blamed them on a spontaneous demonstration stemming from an anti-Islamic video. 

While saying he had not yet discussed the issue with ranking member Elijah Cummings (D-Md.), Gowdy also pointed to deputy national security adviser Ben Rhodes, who wrote a controversial memo. That memo stated that Rice should “underscore that these protests are rooted in an Internet video, and not a broader failure of policy." 

"That memo was pretty important to our understanding of how a false narrative was perpetrated to our fellow citizens," Gowdy said.