A growing chorus of Republican lawmakers is calling for an investigation into House Speaker Nancy Pelosi's accusation that the CIA lied to Congress about Bush-era interrogation techniques.

FBI Director Robert Mueller, when asked if a probe was under way, told Rep. Darrell Issa, R-Calif., on Wednesday that he needed a referral before launching an investigation into the allegation.

So Issa offered one.

"If the CIA is lying to any of us -- and I've been briefed many times by them as a member of the Intelligence Committee -- it puts me in a position of not being able to do my job properly," he said.

Mueller said he would consult with the Justice Department on whether he should investigate the charges.

The exchange is the latest development in a controversy that began with Democrats seeking to hold Bush officials accountable for enhanced interrogation techniques used on terrorism suspects. But Pelosi's contradicting statements on if and when she was briefed on the methods have given Republicans ample ammunition in the partisan conflict.

Rep. Steve King, R-Ill., also called on Mueller to initiate an investigation.

"The CIA and other American defense and intelligence agencies cannot trust Nancy Pelosi without national secrets, let alone our national security, until this matter is resolved," King said in a written statement. "We need an investigation into the basis of Speaker Pelosi's very severe accusations. If true, there has been a serious violation of federal laws. If false, American national security requires a new speaker of the House. The severity of Speaker Pelosi's accusations leaves no middle ground."

Former House Speaker Newt Gingrich went even further, calling on Pelosi to resign. He called her charges "stunning" and "dishonest" and said that she's disqualified herself to be speaker.

But Democrats have circled the wagons around her, some even embracing her accusations.

Only a handful of Republicans are calling on her to step down. That's because most of them are happy to have her as a symbol of the Democratic Party and say privately she is precisely the kind of person they like to run against, a lightning rod and a walking controversy.

One GOP activist told FOX News that as far as Republicans are concerned, her position as speaker has never been more secure.

FOX News' Jim Angle contributed to this report.