This post has been updated with Kelly's commentary on calls for Curiel to recuse himself.

Megyn Kelly describes her rivalry with Bill O'Reilly as a "healthy competition" — one that's mostly about ratings. The Fox News Channel stars host back-to-back prime-time shows and boast the two biggest audiences in cable news. O'Reilly is No. 1 overall, but Kelly beats him some nights and said at Fortune's Most Powerful Women Summit in the fall that "hell yeah" she wants to take over the top spot.

At times, Kelly and O'Reilly have engaged in spirited debates on such subjects as "white privilege" and income inequality. There was even that time last spring when they bickered on-air about how a mutually sought-after guest wound up on Kelly's show and not O'Reilly's.

But their latest clash has nothing to do with Nielsen numbers, political issues or guest appearances. O'Reilly on Tuesday actually jabbed at Kelly's journalism, saying his colleague was "wrong" not to push back against an interview subject who called Donald Trump racist the day before.

O'Reilly played a clip from Monday's episode of "The Kelly File" in which New York City Council Speaker Melissa Mark-Viverito said: "This is an individual, Donald Trump, who is a charlatan and who is racist. What he has done is set up this university, and he has bilked individuals for money."

The university referenced by Mark-Viverito is Trump University, which is the target of a class-action lawsuit alleging fraudulent business practices. Trump, the presumptive Republican presidential nominee, has been complaining about the Mexican American judge presiding over the case, telling the Wall Street Journal last week that the jurist's ethnicity represents an "inherent conflict of interest" because Trump plans to build a wall along the Southern border. He later added that a Muslim judge might be similarly incapable of handling the case fairly.

Kelly cut in when Mark-Viverito stated as fact that Trump "bilked individuals for money."

"He'll have his day in court," the host said, before letting her guest continue.

But that interjection wasn't enough for O'Reilly.

"Ms. Viverito has despised Donald Trump for years," he said Tuesday. "Everybody in New York City knows that, and her charge of racism went unchallenged. That's wrong. Whether it's Trump or Hillary Clinton or President Obama, no ad hominem attacks carry any credibility. They should all be condemned. This racism business is totally out of control, and journalists have a responsibility to rein it in, providing perspective rather than silently allowing the cheap talk."

Kelly has not responded directly to O'Reilly's criticism. But it's worth noting that when she broached the subject of Trump and the judge in an interview with Mike Huckabee later Tuesday night, Kelly was careful to distinguish between the charge that Trump himself is racist and the charge that his comments were racist.

HUCKABEE: Look, anybody that calls Donald Trump racist is — that's nonsense. I mean, there's not a thing—
KELLY: They're saying these are racist comments. Are these racist comments?

It's possible that O'Reilly influenced Kelly to draw such a distinction; it's also possible that she would have done the same thing in her interview with Mark-Viverito the night before but felt she could only cut off her guest to challenge one thing at a time — and thought it more important to push back against the presumption that Trump is guilty of fraud.

One other thing to consider: Kelly also said on her show Monday that "some pundits are demanding that Judge Curiel step down to eliminate doubts as to his motivations, but that is not the way our system works." O'Reilly is one such pundit, so perhaps he viewed Tuesday's critique of Kelly as what Trump would call a counter punch.

In any case, it is apparently unlikely that Kelly and O'Reilly will hash this out in the hallways of Fox News. According to O'Reilly, they rarely cross paths.

"She's in a totally different part of the building," he told the Hollywood Reporter in an interview published Wednesday. "The last time I saw Megyn Kelly was in Detroit in March" at a GOP debate.