Top U.S. intelligence officials are running out of patience with the State Department's reluctance to turn over emails from Hillary Clinton's private email server, which have already been shown to have included top secret communications, Fox News has learned.

The Intelligence Community's Inspector General has requested some 30,000 emails from Clinton's tenure as Secretary of State in order to conduct its own review. Those emails are in possession of the State Department, which has been gradually releasing them to the public.

Clinton has agreed to turn over a similar-sized batch of emails, as well as the highly unusual private server she had installed in her Chappaqua, N.Y., home, to the Department of Justice which is conducting a separate investigation.

An intelligence source told Fox News the State Department has pushed back on the government intelligence watchdog's request, and that Director of National Intelligence James Clapper is considering intervening. The source said the inspector general wants to check the controls on the redaction process and ensure that the office can get a handle on all of the potentially sensitive information that was contained in the Clinton emails.

The flurry of activity came after Charles McCullough, the inspector general, notified senior members of Congress that two of four retroactively classified emails found on Clinton's server were deemed "Top Secret, Sensitive Compartmented Information" — a rating that is the government's highest classifications. 

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Clinton, the former first lady, senator from New York and top diplomat now running for the Democratic presidential nomination, announced Tuesday that she had told aides to turn over the actual server to the Justice Department, giving in to months of demands that she relinquish the device she used to store her correspondence while secretary of state.

Senate Judiciary Committee Chairman Chuck Grassley, R-Iowa, said McCullough had reported the new details about the higher classification to Congress on Tuesday.

The State Department disputes McCullough's determination that the emails were classified at the time they were sent. McCullough had previously told Congress that potentially hundreds of classified emails are among the cache that Clinton provided to the State Department.

A State Department spokesman said Wednesday that the agency is still processing the emails Clinton initially turned over and took a veiled swipe at Grassley for disclosing what McCullough had said.

"The emails that have been discussed have not been released to public," said Deputy Press Secretary Mark Toner. "We are working to resolve if it is indeed classified [and] we are taking steps to make sure the information is protected and stored properly.

"These emails were not marked classified when they were sent," he added.

A source familiar with the investigation told Fox News late Tuesday that the two emails in question contained operational and geospatial intelligence from the CIA and the National Geospatial-Intelligence Agency (NGA), which produces satellite images.

The FBI is investigating whether classified information was improperly sent via and stored on the so-called "home-brew" e-mail server she ran from her home in the New York City suburb after concerns were raised by McCullough. Investigators have said that the probe is not criminal in nature and have denied that Clinton is a target of their inquiries.

Clinton campaign spokesman Nick Merrill said she has "pledged to cooperate with the government's security inquiry, and if there are more questions, we will continue to address them."

It's not clear if the device will yield any information — Clinton's attorney said in March that no emails from the main personal address she used while secretary of state still "reside on the server or on back-up systems associated with the server."

An intelligence source familiar with the matter told Fox News that the campaign's statement of cooperation was overblown, as the FBI had previously taken possession of a thumb drive containing sensitive emails that had been held by Clinton's personal attorney, David Kendall. The Associated Press reported that Kendall gave three thumb drives containing copies of roughly 30,000 work-related emails sent to and from Clinton's personal email address to the FBI after the agency determined he could not remain in possession of the classified information contained in some of the emails.

The AP's report cited a U.S. official briefed on the matter who was not authorized to speak publicly. The State Department previously had said it was comfortable with Kendall keeping the emails at his Washington law office.

Clinton had to this point refused demands from Republican critics to turn over the server to a third party, with Kendall telling the House committee investigating the 2012 attacks in Benghazi, Libya, that "there is no basis to support the proposed third-party review of the server." Clinton has also defended her use of the server, saying she used it as a matter of convenience to limit the number of electronic devices she had to carry.

Congressional Republicans seized on Clinton's reversal late Tuesday.

"It's about time," House Speaker John Boehner, R-Ohio said in a statement. "Secretary Clinton's previous statements that she possessed no classified information were patently untrue. Her mishandling of classified information must be fully investigated."

"Secretary Clinton said she created this unusual email arrangement with herself for 'convenience.' It may have been convenient for her, but it has been troubling at multiple levels for the rest of the country," said Rep. Trey Gowdy, R-S.C., the chairman of the Benghazi select committee. "Secretary Clinton's decision to prioritize her own convenience - and desire for control - over the security of our country's intelligence should concern all people of good conscience."

There is no evidence Clinton used encryption to shield the emails or her personal server from foreign intelligence services or other potentially prying eyes. Kendall has said that Clinton is "actively cooperating" with the FBI inquiry.

In March, Clinton said she exchanged about 60,000 emails in her four years in the Obama administration, about half of which were personal and were discarded. She turned over the other half to the State Department in last December.

The department is reviewing those emails and has begun the process of releasing them to the public.

"As she has said, it is her hope that State and the other agencies involved in the review process will sort out as quickly as possible which emails are appropriate to release to the public, and that the release will be as timely and transparent as possible," Merrill said Tuesday.

Earlier this week, Clinton said in a sworn statement submitted to a federal judge that she has turned over to the State Department all emails from the server "that were or potentially were federal records." The statement, which carries her signature and was signed under penalty of perjury, echoed months of Clinton's past public statements about the matter.

Fox News' Matt Dean and The Associated Press contributed to this report.