On the heels of David Petraeus agreeing to testify on the Libya terror attack, Republican senators on Wednesday stepped up their call to empanel a "select committee" to investigate the tragedy -- as they raised concern that the administration's internal review would fall short.

"Let me be clear: there is no credibility among most of us concerning the administration and the numerous controversies and contradictions that have been involved in their handling of this issue," Sen. John McCain, R-Ariz., said, at a lengthy news conference on Capitol Hill.

McCain was joined by Sens. Lindsey Graham, R-S.C., and Kelly Ayotte, R-N.H., in calling for a temporary Senate committee established specifically to investigate Libya. Senate Democratic Leader Harry Reid later said he would not support their proposal.

The call for what would effectively be a new investigation comes as lawmakers continue to pry into the administration's narrative on what happened before, during and after the attack that killed four Americans. In a victory for lawmakers -- at least those who will hear from him -- Petraeus volunteered to speak to the House and Senate intelligence committees perhaps as early as this week on Libya.

Petraeus had originally been scheduled to testify this Thursday on the burgeoning controversy over the deadly Sept. 11 attack. That appearance was scuttled, though, after the director abruptly resigned over an extramarital affair.

The resignation has since expanded into a sprawling scandal that now includes allegations that Gen. John Allen, the top U.S. commander in Afghanistan, exchanged "inappropriate" and sexually charged emails with Jill Kelley, a Florida socialite linked to the Petraeus case. The rapid developments in the case have all but obscured what until last week was an intense debate on Capitol Hill and beyond over the Benghazi terror attack.

After Petraeus' resignation, lawmakers complained that the scandal was no reason they shouldn't hear from the man at the helm of the CIA when CIA operatives came under attack alongside State Department employees in Benghazi last month.

But a source close to Petraeus said the former four-star general has contacted the CIA, as well as committees in both the House and Senate, to offer his testimony as the former CIA director, and the Senate Intelligence Committee announced he will appear at a closed hearing on Friday to speak about his Libya report. The House side is still being worked out.

Ambassador Chris Stevens and three other Americans were killed in the Sept. 11 attack, which the administration initially blamed on a "spontaneous" mob reacting to protests over an anti-Islam film. Officials later labeled the attack terrorism.

While Petraeus prepares to give his side, lawmakers have begun to openly question when Petraeus first knew about the investigation that uncovered his affair -- and whether it impacted his statements to Congress on Sept. 14 about the Libya terror attack.

Petraeus briefed lawmakers that day that the attack was akin to a flash mob, and some top lawmakers noted to Fox News he seemed "wedded" to the administration's narrative that it was a demonstration spun out of control. The briefing appeared to conflict with one from the FBI and National Counterterrorism Center a day earlier in which officials said the intelligence supported an Al Qaeda or Al Qaeda-affiliated attack.

Rep. Peter King, R-N.Y., told Fox News he now questions whether Petraeus' statements -- which were in conflict with both the FBI briefing and available raw intelligence -- were in any way impacted by the knowledge the FBI was investigating his affair with Broadwell.

King questioned whether the investigation "consciously or subconsciously" affected his statements to Congress.

"It's impossible to believe that he thought he was giving ... honest testimony," King said Wednesday.

Fox News' Catherine Herridge contributed to this report.