The ongoing investigation of former CIA director David Petraeus is “perplexing and suspicious,” according to a leading Republican on the House Government Oversight Committee.

After sending a letter and questioning Attorney General Eric Holder twice and former FBI Director Robert Mueller once about the probe, Rep. Jason Chaffetz, R-Utah, told Holder in a new letter this week, "I find the timeline...to be increasingly perplexing and suspicious. I urge the Department to move forward with this investigation in an expeditious and prudent manner."

Chaffetz also told Gretchen Carlson on Fox News’ “The Real Story” Wednesday that the open investigation may have a chilling effect on the probe by the new Benghazi Select Committee.

"It creates all of this hesitation,” Chaffetz told Carlson. “Both from the Department of Justice and the administration as well as General Petraeus himself, and the reluctance (to provide information) to say ‘well, I can't give you that information, we can't get into that yet, we can't answer questions yet because there's an ongoing investigation.’"

Fox News has been told any testimony by Petraeus would be of keen interest to the Benghazi committee headed by Rep.Trey Gowdy, R-S.C., because the former CIA director can explain a key piece of the puzzle -- what the agency and State Department were doing in in eastern Libya in the days before the attack.

Sources familiar with the Petraeus probe told Fox News that by late spring of 2012, the FBI alerted Petraeus' CIA security detail that his schedule had been compromised after biographer Paula Broadwell sent threatening emails to Florida socialite Jill Kelly over their personal relationships with Petraeus.

A week after President Obama's re-election in November 2012, Petraeus abruptly resigned as CIA Director, citing his extra-martial affair with Broadwell.

As part of the ongoing investigation, Fox News was told FBI agents were probing whether the retired general mishandled or improperly stored classified information.

Last April, Holder was pushed by Chaffetz, at a House Government Oversight Committee hearing to explain why the FBI case was still open.

“When is this going to be complete?” Chaffetz asked Holder.

“It is a matter that is ongoing and we are working diligently to resolve,” the attorney general replied, adding in response to another question that he did not remember when the president was told about the FBI’s investigation of the retired general.

Without responding to specific questions, the Justice Department told Fox News it was reviewing the Chaffetz letter but could not comment on the ongoing investigation of the general.