Laurence Fox's on-air comments about a female journalist were "way past the limits of acceptance" and should have been properly challenged by host Dan Wootton, the boss of GB News has said.
Angelos Frangopoulos told the BBC he was "appalled" by the remarks.
Fox and Wootton have been suspended and the channel is being investigated by Ofcom, which received 7,300 complaints.
Fox sparked the controversy when he asked what "self-respecting man" would "climb into bed" with Ava Evans.
His comments "are not in keeping with the values of us as a business and as a media company", Mr Frangopoulos told Radio 4's Today programme. "And obviously, we took action immediately."
In a combative exchange with Today presenters Amol Rajan and Nick Robinson, Mr Frangopoulos said GB News was following its own investigation process, which would "be completed very soon".
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LISTEN: Angelos Frangopoulos told BBC Radio 4 that Lawrence Fox's comments should not have gone to air
Fox said on Thursday he was "sorry for demeaning" Evans, while Wootton has apologised and said he should have intervened.
Fox added that "I know I'm going to get sacked" on Friday.
Speaking on Friday morning, Mr Frangopoulos said neither Fox nor Wootton had been sacked and that he expected the channel's investigations "to be resolved very quickly".
Fox, who hosts a weekly show on GB News and made the remarks while appearing as a contributor on Wootton's programme on Tuesday, does usually "sail close to the wind", the chief executive said.
"But he didn't sail close to the wind earlier this week. That was way past the limits of acceptance, and that is the difference.
"We are about free speech, but it's about being done in a respectful and proper way, and that was not the way that that conversation played out."
He added that its investigation was "looking very closely at the production process that went into the programme".
He said: "We're looking into the way that the interview was handled. And we're also looking obviously at the comments themselves, which were appalling, and we are absolutely horrified about what was said. I've written a very extensive and personal apology letter to Ava."
He added: "That comment should not have gone to air and that should have been properly challenged, quite frankly."
Mr Frangopoulos said he told Ms Evans in his letter that "it was very unfortunate and does not reflect our values and of course we are very sorry".
On Friday, another GB News presenter, Reverend Calvin Robinson, was also suspended after saying he would not appear on Wootton's show if it was not presented by Wootton himself.
He wrote on social media that the channel's bosses were "scared" of Ofcom and "the woke mob", adding: "If he [Wootton] falls, we all fall."
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Watch: Ava Evans calls insults on GB News 'really nasty' and says she's since received threats online
Challenged by Rajan about whether GB News encouraged Fox "to be controversial [and] to sail close to the wind", Mr Frangopoulos replied: "No, I disagree."
Fox made his name as an actor in TV shows like Inspector Morse spin-off Lewis, and in films like The Hole and Gosford Park.
In recent years he has repositioned himself as a right-wing commentator, activist and aspiring politician but has frequently caused controversy.
He set up the Reclaim Party and stood for election for London mayor in 2021, finishing sixth, and came fourth in the by-election to succeed Boris Johnson as MP for Uxbridge and South Ruislip this July.
On Thursday, Ofcom said it had launched an investigation into whether the GB News broadcast had broken its rules on offence.
The media regulator's chief executive Dame Melanie Dawes told Radio 4's PM programme there were "good reasons to think there may have been a breach".
She said: "Clearly there's been a lot of concern about this and that's why we've actually acted very quickly this week."
Ofcom now has 12 current investigations into GB News, and Mr Frangopoulos rejected the suggestion that the channel did not care about rulings by the watchdog.
"We totally respect Ofcom," he said. "We chose to be regulated. The difference is that what we are doing is very different to what the normal parameters of the Ofcom code were originally considered to be about.
"They were designed for the News at Ten and the Nine O'Clock News," he said. "We are reflecting a different approach to the way that conversations happen and we are disruptive, and that's why Britain is watching this channel."
GB News launched in June 2021, promising to "change the face of news and debate in the UK". It had 2.8 million viewers last month, according to ratings body Barb.
Its editorial charter says it values "freedom of expression but not by causing unjustifiable offence or exposing our audience to harm".
The channel is funded by Dubai-based private investment firm Legatum and hedge fund boss Sir Paul Marshall.
Mr Frangopoulos also defended the decision for Conservative Party deputy chairman Lee Anderson to have Home Secretary Suella Braverman on his weekly show on the channel later.
He told Rajan he was "missing the whole point of what GB News is about". He explained: "We are not journalism for journalists. We're journalism for people, and that is a really big difference.
"The conversations that happen between people like Suella Braverman and Lee Anderson – they are conversations, they're not interviews in the same sense" as on traditional news programmes, he said.
A GB News interview by two other sitting Conservative MPs with the chancellor was recently found to have broken the Ofcom code because it failed to include an "appropriately wide range of significant views".
Meanwhile, the publisher of the MailOnline announced on Thursday it had sacked Wootton, who had previously written a column for the newspaper since 2021, "following events this week".
A DMG Media spokesperson said: "DMG Media can confirm that Dan Wootton's freelance column with MailOnline, which had already been paused, has now been terminated, along with his contract."
The paper had paused the column last month as it announced it was looking into allegations, first reported by the Byline Times, that he used a fake online identity to offer money to individuals for sexually explicit images.
Wootton admitted making "errors of judgment" but strongly denies any criminality.
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