WASHINGTON >> Some of the nation’s intelligence agencies raised alarms last spring as the State Department began releasing emails from Hillary Clinton’s private server, saying that a number of the messages contained information that should be classified top secret.

The diplomats saw things differently and pushed back at the spies.

In the months since, a battle has played out between the State Department and the intelligence agencies — as well as Congress — over what information on Clinton’s private server was classified and what was the routine business of U.S. diplomacy, according to government officials and letters obtained by The New York Times.

At the center of that argument, the officials said, is a top-secret program of the CIA that is anything but secret. It is the agency’s long effort to track and kill suspected terrorists overseas with armed drones, which has been the subject of international debates, numerous newspaper articles, television programs and entire books.

The Obama administration’s decision to keep most internal discussions about that program — including all information about CIA drone strikes in Pakistan — classified at the top-secret level has now become a political liability for Clinton’s presidential campaign.

Some of the skirmishes over Clinton’s emails reflect the disagreements in a post-9/11 era over what should be a government secret and what should not. Nonetheless, 22 emails on Clinton’s server were held back from a tranche made public last week. Those 22 emails were deemed so highly secret that State Department officials in this case agreed with the intelligence agencies not to release them even in redacted form.

The emails are included in seven distinct chains that comprise forwarded messages and replies, and in most cases involved discussions of the CIA drone program, government officials said.

At a Democratic presidential debate in New Hampshire on Thursday night, Clinton dismissed the issue, as she has in the past. She said the government was overzealously classifying information after the fact, citing as evidence the State Department’s finding that two emails sent to Colin L. Powell’s private email account and 10 others sent to the personal accounts of aides to Condoleezza Rice when each served as secretary of state should now be classified years after the fact. It is against the law to have classified information outside a secure government account.

“This just beggars the imagination,” Clinton said, going on to argue that the issue was merely an extension of Republican criticism over the attack against the U.S. consulate and CIA annex in Benghazi, Libya, in 2012.

It remains unknown what exactly the 22 emails contain, given their classification as top secret, but the officials described them generally, on the condition of anonymity. The officials included people familiar with or involved in the handling of the emails in government agencies and in Congress.

Spokesmen and women for the State Department, the CIA and the intelligence agencies’ inspector general declined to comment on the content of the emails.

Some of the emails include material classified at the highest levels, known as Top Secret/SAP, according to a letter sent to the Senate on Jan. 14 by the inspector general of the nation’s intelligence agencies, I. Charles McCullough III. That designation refers to “special access programs,” which are among the government’s most closely guarded secrets.

Several officials said that at least one of the emails contained oblique references to CIA operatives. One of the messages has been given a designation of HCS-O — indicating that the information was derived from human intelligence sources — a detail that was first reported by Fox News. The officials said that none of the emails mention specific names of CIA officers or the spy agency’s sources.

The government officials said that discussions in an email thread about a New York Times article — the officials did not say which article — contained sensitive information about the intelligence surrounding the CIA’s drone activities, particularly in Pakistan.

The officials said that at least one of the 22 emails came from Richard C. Holbrooke, who as the administration’s special envoy for Afghanistan and Pakistan would have been intimately involved in dealing with the ramifications of drone strikes. Holbrooke died in December 2010.

Clinton’s use of a private email server while secretary of state was first disclosed in March, and since then the State Department has slowly released 33,000 emails that Clinton and her aides determined were work-related. None of the emails sent through Clinton’s server were marked as classified, the officials said, and most were written by her aides and forwarded to her. That is also true of the emails forwarded to Powell and Rice, which until now have been in the department’s unclassified archives.

The handling of classified information on Clinton’s server is the subject of an investigation by the FBI, as well as the State Department’s security and intelligence bureaus. According to the law and security procedures Clinton agreed to follow when she became secretary, such material should not even have been sent over the State Department’s official but unclassified state.gov server.

At the same time, the officials said, some of the classifications being sought for the emails fall into a gray area between public knowledge and secrecy. In such instances, the original source of the information — and thus the level of its classification — can be disputed, and has been, vigorously at times, they said. Other emails have been the subject of rigorous debate over what constitutes a secret and what the nation’s diplomats can say about intelligence matters as they grapple with international crises and conflicts.

“While the secretary of state has a duty to protect classified information, as all of us do in a position of trust, here she did not have the benefit of six-plus months of interagency classification reviews,” said Rep. Adam B. Schiff of California, the top Democrat on the House Intelligence Committee. “The same information said by people in two different positions may receive two opposite classification determinations.”

Although the State Department accepted the CIA’s classification of the 22 emails, it has also sought to challenge accusations that it was negligent in handling secrets.

During the review, the State Department has rebutted claims by at least one intelligence agency that information in some of the emails ought to remain classified.

Some of those include the emails that led McCullough’s office to refer the matter to the Justice Department last summer, prompting the FBI’s investigation. McCullough made the referral based on an assessment that four of 40 emails that it sampled early on in the process contained top-secret information.

Now, after months of review, only one of those four turned out to be classified at that level. (The State Department counts that email among the 22 of last week.) A second of the four emails has been downgraded to “confidential,” the lowest level of classification. The third was released last fall.

The fourth involved an email sent by Kurt M. Campbell, the assistant secretary of state for Asian affairs, shortly after a North Korean ballistic missile test in July 2009. The email has not yet been made public, even in redacted form, but the State Department has challenged an assertion from the National Geospatial-Intelligence Agency, which gathers data through satellite images, that the email included information that came from a highly classified program.

In a letter this past Dec. 15 to Sen. Bob Corker, R-Tenn., the chairman of the Senate Foreign Relations Committee, a State Department official said that the information could not have been based on NGA’s intelligence because Campbell did not receive any classified intelligence briefings for what was a new job for him until a few days after the North Korean test.

More broadly, the memo stated, diplomats working at the State Department or in embassies around the world constantly receive and pass on information from unclassified sources — so-called parallel reporting — that can involve highly classified matters. That can make it difficult to determine with confidence whether information in any single email came from a classified source.

“When policy officials obtain information from open sources, ‘think tanks,’ experts, foreign government officials, or others, the fact that some of the information may also have been available through intelligence channels does not mean that the information is necessarily classified,” the department’s assistant secretary for legislative affairs, Julia Frifield, wrote in the December letter to Corker.

Another email whose classification has been disputed was dated April 20, 2011, and was among those that prompted members of Congress and McCullough’s office to begin a review of the State Department’s release of the emails by court order under the Freedom of Information Act.

It was from Timmy T. Davis, an officer in the State Department’s Operations Center, and it conveyed to Clinton’s senior staff security concerns in Libya during the war against the country’s leader, Moammar Gadhafi.

At the time, J. Christopher Stevens, the future ambassador to the country, was secretly traveling there as an envoy to the opposition leadership and had telephoned the Ops Center, as it is known, to advise it about his situation on the ground.

Davis sent his message, marked “SBU,” or “sensitive but unclassified” to two of Clinton’s closest aides, Huma Abedin and Jacob J. Sullivan, as well as to Alice G. Wells, an executive assistant to Clinton who is now the ambassador to Jordan.

At issue were two sentences in the email referring to reports by Africom, the U.S. military command for Africa, describing the movement of Gadhafi’s forces near the city of Ajdabiya. In a letter on Nov. 24 last year, Frifield detailed how the information in the email differed significantly from the suspected intelligence source and could well have been based on public briefings given the day before by NATO’s military about the course of the war.

“The conclusion that the information in the email was drawn from that intelligence product is unsubstantiated and on its face wrong, given the differences between the information in the email and the information in the product,” Frifield wrote.

Even in the case of the drone program, so much information about the strikes has filtered into public that the CIA did not object to every allusion to it, allowing at least vague references in the emails that the State Department has released so far.

In late October 2009, as she prepared for a trip to Pakistan, Clinton asked her aides for good answers to questions she might expect while in the country about Blackwater, the private security company that Pakistanis had long suspected was secretly operating inside the country.

Abedin responded by email that the aides were working on an “answer sheet” for the tough questions she might get on the thorniest issues about U.S.-Pakistani relations — including Blackwater, the security of Pakistan’s nuclear arsenal, and drones.

“You will have tonite or tomorrow am,” Abedin wrote.

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