Graham said that he would be satisfied if Congress had another chance to ask questions of the principal administration officials and Americans on the ground in Benghazi.
"It really does matter that your government tell you the truth about how four Americans died," Graham said. "That would end it for me. I want the survivors to come forward and I want to hear from them what happened."
The South Carolina lawmaker reiterated his call for former Secretary of State Hillary Clinton to testify, and said he believed the former first lady would likely return to Capitol Hill.
"I like Secretary Clinton. I think she's a talented person but when it came to Benghazi, why were all the security requests denied and how could she not know about it?" Graham said.
Earlier Friday, the White House argued that Republicans were pursuing their Benghazi probes for political reasons. In a briefing with reporters, Carney maintained that recently revealed documents indicating the State Department heavily edited talking points originally drafted by the CIA that indicated a possible link to terror groups had been known by congressional Republicans for months.
"If you look at the issue here — the efforts to politicize it were always about were we trying to play down the fact that there was an act of terror and an attack on the embassy," Carney said. "And the problem has always been with that assertion is that it's completely hollow, because the President himself in the Rose Garden said this was an act of terror. And he talked about it within the context of September 11th, 2001. And then we had other officials of the administration refer to this as a terrorist act."