With U.S. intelligence officials scrambling to contain damage from potentially hundreds of spy agency secrets in Hillary Rodham Clinton’s private emails, questions are mounting over why the Justice Departmenthas not yet opened a criminal investigation against the Democratic presidential front-runner for mishandling a mountain of classified information.

While some secrecy experts believe Mrs. Clinton will be able to build a strong case that material on her server was not classified at the time it was moving through her emails, others assert that what the former secretary of state did was far more egregious than the mishandling of information that saw former CIA Director David H. Petraeus sentenced to two years probation and a $100,000 fine.

“I don’t see how the Justice Department would be able to avoid at least investigating this,” said Kevin Carroll, a former CIA officer and secrecy lawyer in Washington. “What Petraeus did was really small in comparison, because there was no exposure of any information to any foreign intelligence services.”

Mr. Petraeus pleaded guilty to improperly handling hard-copy binders of classified military files and sharing them with his mistress and biographer.

“In contrast,” said Mr. Carroll, “it’s certain that foreign intelligence services had access to the stuff on Hillary Clinton’s email.”

“Information put on her home-cooked server and then sent around to other accounts is a very, very serious counterintelligence breach, and they’re going to have to have a really substantial look at the damage that’s been done to every agency that’s had its intelligence compromised,” he said.

But there’s a catch. While officials combing tens of thousands of emails that moved through Mrs. Clinton’s server have pointed to the presence of “hundreds” of pieces of classified information — apparently none of the messages had any official classification markings on them.

It’s a situation that has triggered heated debate over the extent to which such information wasn’t necessarily classified at the time Mrs. Clintonwas emailing it.

“To the best of my understanding, there is no comparison between the Clinton email issue and the Petraeus case,” says Steven Aftergood, who heads the Project on Government Secrecy at the Federation of American Scientists. “Everyone agrees that there was no information in the Clinton emails that was marked as classified. So it would be difficult or impossible to show that those who sent or received the emails knowingly or negligently mishandled classified information.”

“A deeper issue,” according to Mr. Aftergood, “is the subjective nature of classification itself.”

“It is entirely possible for the State Department and the intelligence community to differ about the classification status of a particular item of information,” he said. “If the State Department learned about the information through its own diplomats, it is entitled to consider the information unclassified. If the IC discovered it from a clandestine informant, IC officials would properly deem it classified. So, in a sense, both sides might be right.”

While speculation surges about entire sections that have been redacted or “blacked out” from thousands of pages of emails that the State Department has released from Mrs. Clinton’s private server, at least one email chain appears to contain what Mr. Aftergood described as “diplomatically sensitive” information.

The March 2011 chain, which the department released in June, reveals how Mrs. Clinton’s team was strategizing behind the scenes to try to bring about a “Quad Deal” in which the U.S., Britain, France and Turkey would uphold a no-fly zone in the Middle East — and, more importantly, to make it appear as if Turkey was taking the lead on the initiative.

“I’m worried that [France] and/or the U.K. know about the Turks idea and want to derail it,” states one of the emails, sent to Mrs. Clinton by her then-senior adviser, Jake Sullivan.

Without question, the email offers raw insight into top U.S. officials’ private assessments toward American allies. It also shines a light on the secret diplomatic workings of U.S. policy toward Turkey, and sources have told The Washington Times that Turkish officials were outraged about it upon its release in June.

However, that is not to say the email includes undeniably classified information that came from the U.S. intelligence community — or that American intelligence agencies would now deem it to be damaging.

“Some of the information in the email looks like it could have been diplomatically sensitive at that time,” said Mr. Aftergood. “But all of that information is within the jurisdiction of the State Department to classify or not, as it sees fit. It is hard to see any trace of information in this particular email that might have been obtained from an intelligence agency.”

Mr. Carroll agreed.

“It’s certainly indiscrete, and it would probably be marked SECRET on aState Department or [Pentagon] system,” he said. “But it’s kind of borderline as to whether it’s classified.”

PDB materials included?

But when it comes to sections redacted from other email chains on Mrs. Clinton’s server, intelligence officials appear to have no doubt about the clandestine origin of the most sensitive material lacing the emails.

Last week saw Inspector General for the Director of National Intelligence I. Charles McCullough III — the chief oversight watchdog for the entireU.S. intelligence community — warn in a letter to top lawmakers of the House and Senate intelligence committees that there were “potentially hundreds of classified emails” on the server, at least some of which “included IC-derived classified information and should have been handled as classified.”

The warning also was submitted to the Justice Department, where officials have said no decisions have yet been made about whether to open a criminal investigation.

One former senior Justice Department official, who spoke with The Times on condition of anonymity, said it is possible that intelligence officials referred the case to the department “out of an abundance of caution” in order to avoid being accused of covering something up should there be the kind of highly classified information in the emails that revealed sensitive American intelligence sources.

“We really don’t know the contours of what’s in all these emails yet, so it’s hard to speculate,” the former official said, adding that “the more shocking thing here is just the sheer number of emails that were moving through this server, off the State Department’s secure grid.”

“Secretary Clinton should have said to her staff, ‘Hey, we really need to be careful about what’s being sent around in these emails.’”

Bewildering as such factors may be, Mr. Carroll argues that the more vital issues revolve around the questions of what classified material is actually in the emails — as well as the extent to which it was stored on a server vulnerable to penetration by foreign intelligence services.

“The big issue, I suspect, is the presence or absence of materials derived from the Presidential Daily Brief,” he said.

The PDB, as it is known in intelligence circles, is among the most closely guarded classified documents in Washington — particularly because it often contains revealing information about sourcing that only the highest-level officials in the executive branch are authorized to see.

According to Mr. Carroll, it is well within the bounds of possibility that officials from Mrs. Clinton’s inner circle may have at times stripped the classified markings from information in the PDB and moved it through emails on her server.

“The Justice Department at least has to investigate it,” he said.

While the intelligence warning to lawmakers last week made no specific reference to the PDB, one U.S. official told The Times that the intelligence community has been informed that secret information in some of Mrs. Clinton’s emails originated from the FBI, the DNI and the CIA as well as a spy satellite agency.

The official said the intelligence community’s first response was to take steps to secure the handling of remaining emails and make sure they were handled on top-secret servers to avoid any further breaches, and then to assess any damage to national security from the insecure handling and release of information already in some of the publicly disseminated emails.

“Containment first, then a damage assessment, is how this must be handled,” the official said.

It is believed the emails remain on a thumb drive in the possession ofMrs. Clinton’s private attorney, David Kendall, who declined a request by The Times to comment for this article.

Mr. Kendall is well familiar with the legal implications associated with improper handling of classified materials: He represented Mr. Petraeuslast year.

While the Petraeus case may be very different from Mrs. Clinton’s in detail, there is other precedent by which the Justice Department may pursue a criminal investigation.

Among the more high-profile instances of a former official facing charges for storing classified information on a personal device is one that came in the mid-1990s and involved material on several laptops owned by John M. Deutch, who, at the time, had just retired as director of the CIA.

Mr. Deutch ultimately was pardoned by President Bill Clinton in 2001.

Mr. Carroll, meanwhile, highlighted another case that he has personally been involved in during recent years — representing Maj. Jason Brezler, a 35-year-old reservist who was dismissed from the Marine Corps after emailing a classified document to U.S. military officials in Afghanistan who had requested the document.

Mr. Brezler has sued to challenged his dismissal. His case is pending in federal court.

• John Solomon contributed to this report.