WASHINGTON — Documents released Monday in the Hillary Clinton email investigation show intense disagreement last year between the State Department and the FBI over whether some of Clinton's emails should be considered classified, including a discussion of a possible "quid pro quo" to settle one dispute.

The new batch of documents indicated that in one particular case, a senior State Department official, Patrick F. Kennedy, pressed the FBI to agree that one of Clinton's emails on the 2012 Benghazi attack would be unclassified — and not classified as the bureau wanted.

What remained unclear from the documents was whether it was Kennedy or an FBI official who purportedly offered the "quid pro quo": marking the email unclassified in exchange for the State Department approving the posting of more FBI agents to Iraq.

Officials at both the FBI and the State Department said Monday that no deal had been struck, or even offered, over the classification of Clinton's private emails. They noted that the Benghazi email in question was made public with a sentence blocked out, meeting the FBI's demand for classification. They also said that no additional FBI agents were posted overseas.

There is no indication from the documents that Clinton was aware of the discussion.

Donald Trump and other Republicans nonetheless quickly seized on the new documents as evidence of what House Speaker Paul Ryan called "a cover-up."

The FBI's latest release of 100 pages of internal investigative files prolonged the intense public scrutiny of Clinton's use of a private email server as secretary of state, which has been perhaps more damaging to her presidential campaign than any other issue.

The new documents also cast particular attention on the role of Kennedy, a State Department civil servant for more than four decades, in working to oversee the review and public release of tens of thousands of Clinton's private emails.

One of the FBI reports said State Department employees who reviewed nearly 300 of Clinton's emails on the Benghazi attacks in early 2015 in response to requests from Congress "felt intense pressure" from Kennedy and other senior State Department officials to complete their review quickly and "not label anything as classified."

Kennedy was part of a long-running battle between the State Department and the intelligence agencies over Clinton's emails. As the emails were prepared for release, officials from the intelligence agencies argued in some cases that information in them should have been marked as classified, while State Department officials countered that they contained the routine business of U.S. diplomacy. State Department officials, who argue that the intelligence agencies are overzealous in classifying information, remain sensitive to criticism that they were sloppy in handling the material.

In one of the newly disclosed documents, an unidentified FBI employee told investigators that Kennedy, through another FBI official, had sought in one case "assistance in altering the email's classification in exchange for a 'quid pro quo.'"

The FBI had deemed the email as classified, but the State Department disagreed.

The employee told investigators that "in exchange for marking the email unclassified, State would reciprocate by allowing the FBI to place more Agents in countries where they are presently forbidden," according to the FBI's summary of the employee's questioning by investigators.

A second FBI interview included in the documents provides a somewhat different version of the dispute over the classification of the Benghazi email, with the suggestion that the FBI — and not Kennedy — had offered to make a deal.

In the interview, an unidentified FBI official in the international operations division said Kennedy complained to him that the FBI classification of the document "caused problems for Kennedy" and that Kennedy wanted to give it a different designation and file it in the State Department basement — "never to be seen again."

The unidentified FBI official said he was the one who then "told Kennedy he would look into the email matter if Kennedy would provide authority concerning the FBI's request to increase its personnel in Iraq."

The email they were struggling over was sent on Nov. 18, 2012, by William V. Roebuck, who oversaw the department's office for North Africa at the time and is now the U.S. ambassador to Bahrain.

In it, he notified five other officials of the arrest of "several people" in Libya on suspicion they were connected with the Benghazi attack two months earlier. It was subsequently forwarded to senior officials at the department and then to Clinton on her private email account by her deputy chief of staff, Jake Sullivan, with a short "fyi" note.

Mark C. Toner, a State Department spokesman, said no favors were exchanged in the discussions over Clinton's emails, and there had been no change in the number of agents in Iraq as a result of the conversations.

"The allegation of any kind of quid pro quo is inaccurate and does not align with the facts," Toner said.

The FBI also said there was "never a quid pro quo," but it said the accusations were referred to the bureau's inspection division, which handles internal ethics issues, to investigate. The FBI official who discussed the issue with Kennedy has since left the bureau, an official said.

One of Trump's foreign policy advisers, Michael T. Flynn, a retired general who headed the Defense Intelligence Agency, said the documents provided "undeniable proof" that Clinton "colluded with the FBI, DOJ and State Department to cover up criminal activity at the highest levels."

Two prominent members of the House — Jason Chaffetz, chairman of the Committee on Oversight and Government Reform, and Devin Nunes, chairman of the Permanent Select Committee on Intelligence — called on Secretary of State John Kerry to relieve Kennedy of his position pending an investigation.

In a letter to Kerry, dated Monday, they accused Kennedy, the State Department and the FBI of collusion. They charged that the State Department altered its normal process in reviewing Clinton's emails, consulting directly with the Justice Department and bypassing the FBI's input. A spokesman for Trump's campaign, Jason Miller, said Kennedy should resign.

Toner said Kennedy would remain in his position with the full support of Kerry.

After the email issue emerged in March 2015, Clinton insisted for months that she had never sent or received emails that contained classified information. But she was forced to backtrack, as the FBI concluded this summer that at least 110 emails had contained classified information, even if they had not been marked as such at the time.