Fox News: Republican Trump should apologize after latest Twitter outburst

Kelly was one of the moderators at the network's recent Republican presidential debate, where Trump claimed she asked him unfair questions.

On Monday night, Trump took to Twitter to say Kelly, who had just returned from vacation, was "off her game" and Fox's nightly news program was better without her. He also re-tweeted posts from other Twitter users referring to Kelly as a "bimbo."

"Donald Trump's surprise and unprovoked attack on Megyn Kelly during her show last night is as unacceptable as it is disturbing," Fox News Chairman Roger Ailes said in a statement on Tuesday.

"Donald Trump rarely apologizes, although in this case, he should. We have never been deterred by politicians or anyone else attacking us for doing our job, much less allowed ourselves to be bullied by anyone, and we're certainly not going to start now," he said.

In a statement, Trump responded that he did not think Kelly was a "quality journalist."

"Hopefully in the future I will be proven wrong and she will be able to elevate her standards to a level of professionalism that a network such as Fox deserves," Trump said.

The real estate billionaire accused the network and Kelly of asking him tougher questions than those asked of the other candidates at the Aug. 6 debate. Kelly responded that probing questions were part of her job.

Trump also drew criticism at the time for comments that many people interpreted as suggesting that Kelly was affected by hormones during the debate.

(Reporting by Susan Heavey and Emily Stephenson; Editing by Dan Grebler)