FBI Director James Comey is facing growing Republican calls to launch a perjury probe into whether Hillary Clinton lied under oath about her email use when she testified last year before the House Benghazi committee – even as the Justice Department closes the case on the former secretary of state’s private server.

House Overnight and Government Reform Committee Chairman Jason Chaffetz first urged such a probe during Thursday’s hearing with Comey before his committee. He wants the agency to investigate whether Clinton lied when she told lawmakers “there was nothing marked classified on my emails” – a claim Comey repeatedly contradicted this week.

Comey told Chaffetz a referral from Congress would be needed for an investigation.

“You’ll have one in the next few hours,” Chaffetz said.

When FoxNews.com contacted Chaffetz’s office on Friday, a referral had not yet been sent.

But Chaffetz is vowing to kick-start the process, and his Republican colleagues are voicing support.

Rep. Jim Jordan, R-Ohio, told Fox News a day earlier that Clinton “made statements that [were] directly contradicted by what Mr. Comey’s investigation covered.”

“There are a number of things that she said that are just false based on the investigation Mr. Comey conducted relative to her testimony under oath to us last October,” Jordan said, adding he thinks it would be “appropriate” to look into perjury claims but the decision is ultimately up to Chaffetz and Rep. Trey Gowdy, who chairs the Benghazi committee.

It was during an exchange with Gowdy that Comey on Thursday countered several statements Clinton had made, both in public and before the Benghazi committee.

Notably, he said her statement that nothing she sent or received was marked classified was not true. To the contrary, Comey confirmed the FBI's investigation found at least three emails with classified markings on Clinton's server.

The State Department says human error was responsible for those markings. In a statement after Thursday’s hearing, Clinton spokesman Brian Fallon claimed Comey’s testimony “clearly knocked down a number of false Republican talking points and reconciled apparent contradictions between his previous remarks and Hillary Clinton's public statements.”

Yet the stepped-up calls to dig deeper into Clinton’s statements signal the investigations concerning Clinton’s conduct in office are not over – even as lawmakers on Friday approved a final report on the deadly 2012 attacks in Benghazi, Libya.

The two-year inquiry, among many other details, had revealed she used a private email server for government business, setting off intense scrutiny that continues to dog Clinton's presidential campaign. The 7-4 vote to approve the 800-page report was split along party lines, reflecting partisanship that emerged after the panel's creation in May 2014 and escalated in this election year. Democrats have submitted their own report on the attacks, which killed four Americans, including U.S. ambassador Chris Stevens.

Gowdy, R-S.C., echoing Chaffetz, also said lawmakers may seek a federal investigation into whether Clinton lied to the committee in testimony last year.

"Our committee has an obligation" to report any untruthful testimony to the FBI, Gowdy said.

Asked if he was referring to Clinton, Gowdy said, "She's one of 100 witnesses."

Under oath, Clinton testified last October that she never sent or received emails marked as classified when she served as secretary of state. She also said she only used one mobile device for emails and turned over all of her work-related emails to the State Department, claims Comey also contradicted on Thursday.

Separately, the State Department is reopening its internal investigation of possible mishandling of classified information by Clinton and top aides. The internal review was suspended in April to avoid interfering with the FBI inquiry.

House Democratic leader Nancy Pelosi dismissed the latest GOP move as purely political.

"So let's get this straight: This is going to be an investigation of the decision that is an investigation of the emails that was part of the investigation of Benghazi," she told reporters.

Rep. Elijah Cummings of Maryland, the senior Democrat on both the Benghazi and Oversight panels, said an FBI referral was "unwarranted," since Comey said only three emails out of more than 30,000 sent or received by Clinton contained classified markings.

Comey said Thursday that his team found no evidence that Clinton lied under oath to the FBI or broke the law by discussing classified information in an unclassified setting.

Under an onslaught of Republican criticism, Comey vigorously defended the government's decision and rejected GOP accusations that the presidential candidate was given special treatment.

To criminally charge Clinton based on the facts his agency's yearlong probe had found would have been unwarranted and mere "celebrity-hunting," Comey said.

The Associated Press contributed to this report.