Megyn Kelly says she will not be cowed by Donald Trump's criticism of her

Mr Trump has come under fire after comments that suggested the Fox News journalist had blood 'coming out' of her

Megyn Kelly interrupted the broadcast (YouTube )

It’s fair to say Donald Trump and Megyn Kelly won’t be going for a carriage ride in Central Park anytime soon.

Four days after the pair clashed when she questioned him during the Republican debate (and three days after he sparked outcry by suggesting she was having her period), Ms Kelly addressed the spat for the first time.

“I certainly will not apologise for doing good journalism, so I’ll continue doing my job without fear or favour,” she said during the Monday night broadcast of her Fox News show The Kelly File.

She added: “This is a tough business and it’s time now to move forward.”

Pundits generally reckoned that the 44-year-old anchor generally had the better of the billionaire tycoon during last Thursday’s event when she asked him about comments he had made about women that included “fat pigs”, “dogs” and “slobs”.

Mr Trump, 69, hit back by saying the US did not have time for political correctness, and in the subsequent days the tycoon’s supporters appeared to prove his assertion by attacking the journalist on social media.

He then triggered further anger by claiming Mr Kelly had “blood coming out of her eyes. Blood coming out of her wherever.”

Despite the outcry he had triggered Mr Trump has declined to say sorry. On Monday, he went as far as to suggested that Ms Kelly should be the one apologising to him.

And on Tuesday morning he kept up his fists, telling CNN that the only people who could interpret his comments as relating to Ms Kelly’s period were those with a “deviant” mind.

“Most people agree with what I said,” said Mr Trump, who is leading the field of Republican candidates in the polls. “What I said was very clear.”

He added: “I will be so good for women. I will cherish women.”

Fox News Chairman and CEO Roger Ailes spoke with Mr Trump directly on Monday, assuring him he will “treated fairly” by the station, the tycoon tweeted on Monday.

“Roger Ailes just called. He is a great guy & assures me that Trump will be treated fairly on @FoxNews. His word is always good!” wrote Mr Trump.

In a statement issued on Monday evening, Mr Ailes said the air had been cleared and said the conversation was “blunt but cordial”. He described Ms Kelly as a “brilliant journalist”, whom he fully supported. The anchor is considered one of the network's star performers and currently secures the second-highest audience.

“Donald Trump and I spoke today,” he said. “We discussed our concerns, and I again expressed my confidence in Megyn Kelly.”