Rep. Paul Gosar, R-Prescott, said FBI Director James Comey should have recommended that former Secretary of State Hillary Clinton be prosecuted for mishandling State Department emails.
Director Comey went on to say that he thought that the hearing was good for transparency and democracy, but throughout his testimony, Comey has largely backed up what Hillary Clinton has been saying about her use of private email.
Comey pointed out that Petraeus not only shared the classified information, but also hid the documents in his attic and then lied to investigators.
"Should have known, must have known, had to know, does not get you there", he said. "There would be some discipline".
In almost five hours of testimony, Comey sought to explain the Justice Department's decision ending an investigation that has dogged Clinton's presidential campaign and raised fresh questions among voters about her trustworthiness.
Many Republicans - and, especially, Donald Trump - immediately claimed that "the system was fixed" on behalf of Clinton.
Separately, the U.S. State Department is reopening an internal investigation into whether Clinton and her top aides mishandled classified information when she was serving as the secretary of state under President Barack Obama.
The State Department suspended its review in April to avoid interfering with the FBI's inquiry.
"We will aim to be as expeditious as possible, but we will not put artificial deadlines on the process", State Department spokesman John Kirby said Thursday, noting that the internal review can proceed now that the Justice Department investigation wrapped up with no charges filed against Clinton.
"In their (Republicans') eyes, you had one job and one job only: to prosecute Hillary Clinton", said Rep. Elijah Cummings, D-Maryland, to Comey.
Many of Clinton's political critics have suggested that her use of private email servers could have endangered national security by exposing classified information to potential hacking. To criminally charge Clinton based on the facts the FBI's yearlong probe had found, would have been unwarranted and mere "celebrity-hunting", he said.
In the aftermath of FBI Director' James Comey's assessment, President Obama expressed concern over the State Department's sloppy and cavalier handling of classified information during the years Hillary Clinton was secretary of state.
'The question I always look at is, is there evidence that would establish beyond a reasonable doubt that somebody engaged in conduct that violated a criminal statute.
As I was watching Comey's recitation of the facts of the case, I was thinking that he was going to recommend a non-prosecution simply because he publicly stated the essence of the FBI's investigation, and therefore, he was precluding any jury's hearing the case.
Comey also testified that there were three emails found on Clinton's servers bearing the letter "C" which denotes they were classified, in apparent contradiction of the former secretary of state's statements.
Comey said investigators had no basis to believe that Clinton lied to the Federal Bureau of Investigation during a 3-1/2 hour interview last Saturday, but Gosar and others are calling for perjury charges against Clinton for these remarks.