The Justice Department said Friday that it has been notified of a potential compromise of classified information in connection with the private e-mail account that Hillary Rodham Clinton used while serving as secretary of state.

A Justice official said the department had received a “referral” on the matter, which the inspector general of the intelligence agencies later acknowledged came from him.

The inspector general, I. Charles McCullough III, said in a separate statement that he had found information that should have been designated as classified in four e-mails out of a “limited sample” of 40 that his agency reviewed. As a result, he said, he made the “security referral,” acting under a federal law that requires alerting the FBI to any potential compromises of national security information.

“The main purpose of the referral was to notify security officials that classified information may exist on at least one private server and thumb drive that are not in the government’s possession,” McCullough said in a statement, which was also signed by the State Department’s inspector general, Steve A. Linick.

The private server is Clinton’s, and the thumb drive, containing 30,000 e-mails she turned over to the State Department, is in the possession of her attorney, David Kendall.

Catch up on the controversy and read the emails

The statements — prompted by inaccurate media reports that the Justice Department was weighing a “criminal” investigation related to the Clinton e-mails — marked the latest turn in an increasingly acrimonious partisan battle over Clinton’s tenure at the State Department.

Republicans have said they want a full accounting of her actions related to the 2012 attack in Benghazi, Libya, in which Islamist militants killed four Americans, including Ambassador J. Christopher Stevens. Democrats have said the GOP is using a House select committee on the terrorist attack to undermine Clinton’s presidential campaign.

The Justice Department’s involvement added a new layer to the controversy, reflecting a turf battle over classification standards between intelligence agencies and the State Department officials reviewing the e-mails for release to Congress and the public.

Officials acknowledged that none of the e-mails reviewed so far contain information that was marked classified when they were sent. But a new inquiry would prolong the political controversy Clinton is facing over her un­or­tho­dox e-mail system.

The private e-mail system, maintained outside of direct government control, is a reminder of the investigations that were a constant feature of her husband’s presidency. It also has invited questions about whether she bent rules or regarded herself as above them, feeding voter unease about her trustworthiness.

At a New York campaign event Friday, Clinton referred only briefly to the controversy, saying that “there have been a lot of inaccuracies” and joking that “maybe the heat is getting to everybody.”

“We all have a responsibility to get this right,” Clinton said. “I have released 55,000 pages of e-mails” that have been handed over to the State Department.

The controversy began late Thursday with a New York Times report that “two inspectors general have asked the Justice Department to open a criminal investigation” into whether sensitive government information was mishandled in connection with Clinton’s e-mails.

On Friday morning, a Justice Department official initially confirmed the report to The Washington Post and to other media outlets.

Rep. Trey Gowdy (R-S.C.), chairman of the House Select Committee on Benghazi, issued a statement soon after saying that “the only way” to resolve the concerns was for Clinton’s private e-mail server to be “voluntarily relinquished or acquired by other lawful means” for forensic examination.

Responding with a statement of his own, Rep. Elijah E. Cummings, the panel’s ranking Democrat, said he had spoken to Linick, the State Department’s inspector general, who said that “he never asked the Justice Department to launch a criminal investigation of Secretary Clinton’s e-mail usage.” Later in the day, the Justice Department backed away from its characterization of the referral as “criminal.”

Cummings (Md.) called the basis for the media reports “the latest example in a series of inaccurate leaks to generate false front-page headlines — only to be corrected later — and they have absolutely nothing to do with the attacks in Benghazi or protecting our diplomatic corps overseas.”

Cummings also released a Thursday memo sent by McCullough, the inspector general of the intelligence agencies, to the chairmen and ranking minority-party members of the House and Senate Intelligence Committees.

In the memo, McCullough acknowledged that his office had been informed late last month by the State Department “that there are potentially hundreds of classified e-mails within the approximately 30,000 provided by former Secretary Clinton.”

None of those reviewed by his office “had classification or dissemination markings, but some included” intelligence-community information “and should have been handled as classified, appropriately marked, and transmitted via a secure network,” McCullough wrote.

“Further, my office’s limited sampling of 40 of the emails revealed four contained classified [intelligence community] information which should have been marked and handled at the SECRET level.” The information, he said, had not been “retroactively classified” by the State Department.

The 30,000 e-mails “are purported to have been copied to a thumb drive in the possession of former Secretary Clinton’s personal counsel, Williams and Connelly attorney David Kendall.”

Kendall, who formerly served as counsel for ex-CIA director David H. Petraeus, has a security clearance. He declined to comment on the matter Friday.

About 3,000 of 55,000 pages of Clinton e-mails — sought by both the Benghazi committee and a number of Freedom of Information Act requests — were released in late June. Portions of two dozen of the e-mails, which officials said had been retroactively classified, were redacted.

The rest are still being reviewed by a group of retired Foreign Service officers brought in by the State Department for the task. More releases are pending under a court order for expeditious processing.

In his Thursday memo to Congress, McCullough said that State had agreed to his recommendation that intelligence officials be involved in the review process. But he said a request for State to give the intelligence community a copy of all the e-mails had been “rejected on jurisdictional grounds.”

McCullough said he also recommended that freedom-of-information officials at the State Department implement “a dispute resolution process in regard to differences of opinion about classification levels and exemptions.” He said that “State has not yet provided sufficient information for us to close this recommendation.”

The existence of Clinton’s private e-mail server was revealed in March by the New York Times. At the time, Clinton said that she was “certainly well aware of the classification requirements and did not send classified e-mail.”

Earlier this week, Quinnipiac University released polling from Colorado, Iowa and Virginia — all key states in the presidential election — indicating that Clinton’s favorability ratings and her marks for trustworthiness have dropped considerably since the controversy began in April.

Clinton’s campaign pushed back quickly Friday against the suggestion that concerns by the inspectors general raised any deeper questions about her online exchanges. Spokesman Nick Merrill said that she had “followed appropriate practices in dealing with classified materials.”

Karen Tumulty contributed to this report.