The State Department on Monday deemed 23 more of former Secretary Hillary Clinton’s emails “secret,” more than doubling the number of messages she sent or received on her special account that have now been given that high level of classification.

Those messages were part of the last batch of 1,700 or so Clinton emails released by the State Department on Monday, closing out a 14-month process in which the department, under a judge’s order, processed and released 30,322 messages from Mrs. Clinton’s secret server.

Of those messages, a total of 45 have been deemed to contain “secret” information and more than 2,000 have “confidential” information — the lowest level of classification. More than 20 other messages were already labeled “top secret” and withheld entirely, bringing the overall classification level for Mrs. Clinton’s account to 6.8 percent, or about one out of every 14 messages she handled.

“On more than 2,000 occasions, Hillary Clinton recklessly jeopardized our national security and sensitive diplomatic efforts by using a secret, unsecure email server to send and receive classified material,” Republican National Committee Chairman Reince Priebus said in a statement accusing Mrs. Clinton of “a clear attempt to skirt government transparency laws.”

Mrs. Clinton declined to use an email tied to her department’s official State.gov system and instead created an account on a server she maintained at her home in New York, under the domain name clintonemail.com.

That arrangement, which the department has since said was against its policy, meant many of her messages were not archived and searched as required by law in response to requests from Congress, subpoenas from courts or Freedom of Information Act requests from the public.

After prodding by the congressional probe investigating the 2012 Benghazi terrorist attack, Mrs. Clinton in December 2014 turned back to the State Department about 32,000 messages she said she sent or received during her time in office and that she deemed to be public business. She declined to turn over another 30,000 or so messages she said were purely personal.

Of the 32,000 messages she did produce, the National Archives says more than 1,000 of them are not related to government business, and they have been withheld.

Releasing the others has been a major headache for the Obama administration, which missed court deadlines and refereed internal fights over whether, and how, to withhold information that the government now deems classified.

The State Department and the intelligence community reached an agreement Monday on one message, upgrading it from “top secret” to merely “secret” after deciding the original assessment was not correct.

“The information available to diplomats and the judgments they form do not necessarily need to be classified just because there are parallel intelligence sources,” State Department spokesman John Kirby told reporters.

That’s a small victory for Mrs. Clinton, who has argued that the Obama administration has gone overboard on classification. She has called for all of her messages to be released to the public.

She also says none of the messages she sent or received contained information marked classified at the time she handled the email.

Many of the secret-level emails released Monday contain readouts of conversations other people had with foreign leaders. Several of the messages involved current Secretary of State John F. Kerry, who at the time was chairman of the Senate Foreign Relations Committee and sent information from meetings he had with top foreign officials.

Mr. Kerry faced questions about the messages while testifying on Capitol Hill last week, saying he was unaware that he was emailing an account not tied to the official State.gov server.

“I didn’t think about it. I didn’t know if she had an account, or what the department gave her at that point in time, or what she was operating with,” he said. “I had no knowledge.”

Also among the “secret” emails released Monday is a document from Clinton confidant Sidney Blumenthal, whom Mrs. Clinton has tried to distance herself from during her campaign for the Democratic presidential nomination. The April 24, 2010, series of messages includes a long memo from a friend that Mr. Blumenthal forwarded detailing thoughts about Kyrgyzstan.

Another 2011 memo from Mr. Blumenthal to Mrs. Clinton concerning the strife in Libya may have even made its way to the White House — though without Mr. Blumenthal’s fingerprints.

Mrs. Clinton, in forwarding the memo to top aide Jacob Sullivan, said: “This is informative. Should we pass on (unidentified) to WH +/or other agencies?”

Mr. Blumenthal was so detested by the White House for his role in attacking Barack Obama in the 2008 presidential primary season that Mrs. Clinton was forbidden from hiring him at the State Department. He instead appears to have been an active secret informant for her.

Another secret message details the State Department’s public relations strategy in handling a New York Times report on an Afghanistan reconstruction project in which U.S. money may have been sent to a Taliban ally to pay for security for the road project. According to the emails, The Times agreed to delay the story out of concern for harming national security. The part of the message deemed classified dealt with the FBI, which was alerted to suspected problems after The Times’ inquiry.

The release of the last batch of emails Monday does not close the controversy over Mrs. Clinton’s account.

Judicial Watch, a conservative public interest law firm, has asked a federal judge to order Mrs. Clinton to turn over her entire email account, including the 30,000 or so messages that she deemed private business.

Judge Emmet G. Sullivan last week said he is “inclined” to agree with that request and in the meantime has granted Judicial Watch discovery in the case, meaning the group will be able to prod Mrs. Clinton’s top aides about who approved her account, how it was maintained and how she decided which messages to turn over to the government.

In addition to the nearly two dozen top-secret documents withheld in their entirety, the State Department declined to release 19 messages Mrs. Clinton exchanged with President Obama via her secret account.

The department also said it is withholding one other one-page message that, while not classified, contains information that a law enforcement agency does not want made public.

“Beyond that, I can’t speak to the contents of it, as the decision has been made to deny in full, but as you guys well know, that is not uncommon when dealing with Freedom of Information Act requests,” Mr. Kirby told reporters.

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