It continued: “CNN reserves the right to publish his identity should any of that change.”
The last line struck critics as sinister or as a veiled threat, a characterization Mr. Kaczynski strongly denied on Twitter. A hashtag, #CNNBlackmail, lit up among people, especially on the right, claiming CNN was pressuring the Reddit user not to mock the network again.
In another tweet, Mr. Kaczynski said the Reddit user had called him after the story’s publication and told him: “I am in total agreement with your statement. I was not threatened in anyway.”
Some critics, including Donald Trump Jr., referred to the Reddit user as a 15-year-old, but it was not clear what that conclusion was based on. Mr. Kaczynski flatly denied the claim, saying that the user was an adult and that Mr. Trump and others were intentionally “spreading misinformation.”
The network has been a frequent target of attacks from the right as it covers the Trump administration.
Ted Cruz, the Republican senator, said CNN’s story was “troubling” and suggested it could be seen as extortion.
In a statement, Matt Dornic, a spokesman for the network, said that “CNN decided not to publish the name of the Reddit user out of concern for his safety,” and that “any assertion that the network blackmailed or coerced him is false.”
The user apologized and deleted his Reddit account before speaking with Mr. Kaczynski, the statement said.
“CNN never made any deal, of any kind, with the user,” Mr. Dornic said. “In fact, CNN included its decision to withhold the user’s identity in an effort to be completely transparent that there was no deal.”
While the right-wing critics seized on an opportunity to target CNN, journalists debated the always-thorny issue of granting anonymity. Some thought the Reddit user should have been identified, while others questioned the conditions CNN appeared to impose on allowing the user to remain anonymous.
Andrew Seaman, the ethics chair of the Society for Professional Journalists, said in a blog post that tying the source’s anonymity to future behavior was odd, but not unethical.
“Journalists should support the open and civil exchange of views, but their role is debatable when they try to police good conduct on other platforms,” he wrote. “Additionally, where would these types of agreements with sources end? Would journalists agree not to identify a thief because he or she promised never to steal again?”
Readers often greet anonymous sources with suspicion, and journalism ethicists often scrutinize the practice, but newsrooms still rely on them when significant stories would otherwise go untold. In most cases, as when someone is in a war zone or is discussing sensitive political matters, anonymity is granted because the sources fear retribution that would compromise their physical safety or have professional consequences.
Indira Lakshmanan, the Newmark chair in journalism ethics at the nonprofit Poynter Institute, said the CNN story was newsworthy and that there were legitimate reasons to shield the Reddit user’s identity, since journalists have a responsibility to minimize harm to private citizens.
But she said the condition of the anonymity in the CNN story was “awkwardly written,” unusual and unnecessary.
“There are a whole host of reasons we protect identities,” she said. “The whole reason of someone stepping out of line is not usually one of those things.”
Ben Smith, the editor in chief of BuzzFeed, where Mr. Kaczynski used to work, defended his former reporter, as did the conservative radio host Hugh Hewitt.