By SHANE HARRIS Updated Jan. 16, 2017 10:39 p.m. ET Outgoing Central Intelligence Agency Director John Brennan on Monday rejected Donald Trump’s suggestions that he may have leaked an unsubstantiated dossier on the president-elect while defending the U.S. intelligence community more broadly from Mr. Trump’s recent attacks on its credibility and integrity.

Mr. Brennan said he had no way to assess the allegations contained in the dossier of political opposition research, which included inflammatory personal information and suggestions of contacts between Mr. Trump and the Russian government. The dossier was published last week, days after U.S. officials had informed Mr. Trump of its existence.

Mr. Trump appeared to take direct aim at Mr. Brennan in a Twittermessage Sunday night, asking of Mr. Brennan: “Was this the leaker of Fake News?”

“Was I a leaker of this? No,” Mr. Brennan said Monday in an interview at CIA headquarters, days before he ends a career that has spanned more than three decades and that took him from entry-level recruit to head of the nation’s most storied spy service.

“First of all, this is not intelligence community information,” Mr. Brennan said. He noted that the dossier had been circulating “many months” and that he first heard about it from inquiring reporters last fall. To date, he hasn’t read the document and gave it no particular credence, he said.

“I would have no interest in trying to give that dossier any additional airtime,” Mr. Brennan said.

The dossier was compiled by a former British intelligence officer, Christopher Steele. Mr. Brennan noted that it was the Federal Bureau of Investigation’s responsibility to investigate any potential links between Russians and U.S. citizens. And, he said, it was the FBI that decided to inform Mr. Trump of the dossier’s existence on Jan. 6, during a classified briefing in New York.

“There was an interest on the part of the bureau to make sure that the president-elect was aware of and informed of” the dossier, Mr. Brennan said. “It was not part of the [hacking] report. And it was very explicitly stated that the conclusions of this report in no way took that information [from the dossier] into account. The feeling was wanting to make sure that given the very salacious nature of it, the president-elect was at least aware of it so he could take it into account and do what needs to be done.”

Other officials familiar with the briefing of Mr. Trump said Monday all the agencies involved agreed the issue of the dossier should be raised.

While Mr. Brennan brushed off Mr. Trump’s dig at him personally, he was indignant at the president-elect’s attack on his fellow spies. In recent weeks, Mr. Trump has accused them of botching their analysis on the Russian hacking campaign and accused them of leaking pieces of their conclusions for political gain.

“I think it’s the right and indeed the responsibility of the president of the United States to challenge the conclusions of the intelligence community,” Mr. Brennan said. “We don’t expect our information and our assessments to be swallowed whole.

“It’s when there are allegations made about leaking or about dishonesty or a lack of integrity, that’s where I think the line is crossed,” he continued, taking particular umbrage at Mr. Trump’s comments last week that leaking intelligence on political figures was something that Nazi Germany “would have done and did do.”

“Tell the families of those 117 CIA officers who are forever memorialized on our wall of honor that their loved ones who gave their lives were akin to Nazis,” Mr. Brennan said. “Tell the CIA officers who are serving in harm’s way right now and their families who are worried about them that they are akin to Nazi Germany. I found that to be very repugnant, and I will forever stand up for the integrity and patriotism of my officers who have done much over the years to sacrifice for their fellow citizens.”

Mr. Trump’s aides didn’t respond to requests Monday night for comment.

In his nearly four-year tenure as director, Mr. Brennan has attracted his share of criticism, particularly for a sweeping overhaul of the CIA’s organizational structure, which has upset a bureaucracy that frequently doesn’t welcome change. But it was clear from his parting remarks, in what is expected to be his final interview as director, that Mr. Brennan would prefer his legacy be the way he fought to nurture a workforce that reflected America’s diversity.

During his tenure he has put particular emphasis on promoting the interests of gay, lesbian, and transgender officers. He was the first CIA director to attend an annual social gathering of LGBTQ employees and has been known to wear a rainbow lanyard around the office as a symbol of solidarity.

For Mr. Brennan, who said his perspective was informed by growing up “a white male from New Jersey,” diversity of backgrounds leads to better analysis, which in his estimation can prevent intelligence disasters. “I just think that having those varied perspectives really adds great color and dimension and diversity to how we look at problems,” he said. “It gets us away from groupthink.”

Mr. Brennan said he spent Monday morning making farewell phone calls to about a dozen foreign counterparts, including Alexander Bortnikov, the director of Russia’s Federal Security Service, or FSB, with whom he has had a relationship the past four years. While it has grown “very tense” of late, Mr. Brennan said the final call was reassuring.

“What I told him this morning was, despite the unpleasantness that we’ve had and despite the differences in a number of the policies of our government, that I very much hope that the CIA and the Russian intelligence services can work together in the future,” Mr. Brennan said, particularly on counterterrorism.

“I told him and reassured him that any intelligence we get about threats to Russian people or the Russian homeland we will immediately make it available to them. And he agreed and said they would do the same thing,” Mr. Brennan said.

Later this week, Mr. Brennan will host a ceremony honoring the Rev. Martin Luther King Jr. and celebrating diversity initiatives. Then will come a final farewell speech to the CIA workforce.

On Friday at noon, Mr. Brennan will cease to be a CIA officer. He said he might spend that morning in his office, alone.

“I don’t know what I’m going to do. Because this will be the last time that I serve in this agency,” Mr. Brennan said. “I will linger by the Memorial Wall.” His voice tightened, and his eyes misted. He paused. “It gets real.”

With that, he forced a smile, and said the next thing he hoped to do was see a movie. “I hear they’re in color now. It’s been a while.”

Write to Shane Harris at share.harris@wsj.com