The feud between Fox News anchors Bill O’Reilly and Megyn Kelly has ratcheted up in recent days following a series of separate interviews the pair conducted this week.

O’Reilly, who is promoting his new children’s book Give Please a Chance, declined to respond earlier this week when asked in an interview about sexual harassment allegations leveled against former Fox News chief Roger Ailes in Kelly’s just-released first memoir, Settle For More.

In her book, Kelly accused Ailes of making “inappropriate sexually-charged comments” to her during private meetings, and later alleged that the longtime network executive grabbed her and attempted to kiss her on the lips.

“I’m not interested in basically litigating something that is finished that makes my network look bad, okay?” O’Reilly told CBS This Morning co-host Norah O’Donnell on Tuesday. “I’m not interested in making my network look bad at all. That doesn’t interest me one bit.”

O’Reilly revisited the subject on his primetime Fox News show Tuesday night.

“If somebody is paying you a wage, you owe that person or company allegiance. You don’t like what’s happening in the workplace, go to human resources or leave,” the anchor said, without mentioning Kelly by name. “I’ve done that. And then take the action you need to take afterward if you feel aggrieved. There are labor laws in this country. But don’t run down the concern that supports you by trying to undermine it.”

In a Wednesday appearance on 77WABC Radio, O’Reilly appeared to soften his position, calling Kelly a “very smart, talented woman,” who “has a perfect right to write a book and say anything she wants to say. And I don’t want that to get lost.”

“So I don’t have any beef. She runs her career, I run my career,” he went on to say. “But when a network is… going to try and bait me to say bad things about my network, I am not gonna do it.”

In a TV interview Wednesday morning, Kelly said it was not her that was making Fox News “look bad.”

“I think Roger Ailes is making the company look bad,” Kelly said on CBS This Morning when asked about O’Reilly comments.

I’m trying to shine a light on this,” she added. “And put other companies on notice that we’re watching you.”

In a separate interview with the Hollywood Reporter published Wednesday, Kelly acknowledged that the relationship between her and O’Reilly had grown “more competitive” over the years.

“And that is just true of us as personalities,” she explained. “Again, as with Hannity, we are both Irish, we’re both Catholic, and we’re both very competitive. So the dynamic has changed. But I really will always be grateful to Bill.”

Kelly’s book has not faired well among Amazon reviewers in the early days of its release.

On Wednesday, the online retailer notes some 73 percent of the reviews of Kelly’s new book gave it a one-star rating. Another 22 percent rated the book five stars.

Still, Kelly’s memoir currently sits at the top of Amazon’s bestseller’s list.

Follow Jerome Hudson on Twitter @jeromeehudson