Melbourne-based Bolt, a newspaper columnist, blogger and Sky Television host, has demanded Sydney radio 2GB mornings host Ray Hadley apologise for calling him "creepy" for defending the cardinal.

But Hadley said Bolt was wrong because he only called him "creepy" in reference to a separate case concerning a pedophile.

"I won't be apologising for calling him 'creepy' in relation to Pell because I did not," Hadley thundered at the start of his 9am show on Wednesday.

"So Mr Bolt don't hold your breath ... check your facts."

Hadley then told his audience Bolt was on his open phone line before saying "you've had your say" and declining the call.

At 9.25am, Bolt hit back on his Herald-Sun blog, saying "Ray Hadley is a coward."

"I asked to go on air for a right of reply but he refused."

Bolt said he tried again to get on air and spoke to a Hadley program staffer.

"Once again Ray refused to take my call, and then went on air again to accuse me of bullying his staffer. Falsely claimed I said I would have his staffer sacked."

Bolt admitted telling the staffer he should be ashamed of working for Hadley and that "I would remember him", according to his blog post.

The furore began when Bolt spoke to Hadley's 2GB stablemate, breakfast host Alan Jones, just before 9am and demanded the apology.

The pair had been discussing the outcome of a High Court hearing into the Pell case.

The court on Tuesday acquitted Cardinal Pell of five child sexual abuse offences because there was "a significant possibility that an innocent person has been convicted because the evidence did not establish guilt to the requisite standard of proof".

Cardinal Pell spent more than 400 days - first in Melbourne's Metropolitan Remand Centre and later the maximum security Barwon Prison - in jail before he was released within hours of the High Court judgment.

Australian Associated Press