Prime Minister Scott Morrison says he doesn’t understand why people are “tying themselves up in knots” about a plan to project an advertisement for a lucrative horse race on the sails of the Opera House.

Mr Morrison spoke with Sydney radio heavyweight Alan Jones on Monday morning, after Mr Jones lobbied for the Racing NSW ad to go ahead.

Opera House management originally said no to the Everest Cup ad, but was overruled by NSW Premier Gladys Berejiklian after intense advocacy from Mr Jones on his 2GB radio show.

“I just don’t understand why we’re tying ourselves up in knots about this,” Mr Morrison told the broadcaster on Monday morning.

“It’s not like they’re painting it up there.”

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On Friday, Ms Berejiklian ordered Opera House management to allow the advertising, saying “timeliness” was an issue ahead of the race itself on Tuesday.

Mr Morrison entered the fray on the weekend, saying the Opera House was the “biggest billboard Sydney has”.

Opposition leader Bill Shorten said he “liked” horse racing and was proud to be the local member in the electorate that hosts the Melbourne Cup.

But he said Mr Morrison had not shown the Opera House the “respect” it deserved as a national icon.

“I don't think most Australians, when they think about the Opera House, think of it as a billboard, Mr Shorten told reporters on Monday.

'Desecration'

The promotion includes showing the barrier draw on the sails and images of the Everest Cup itself.

As of Monday morning, more than 120,000 people had signed a change.org petition to "protect" the iconoic building from "Alan Jones and his Gambling mates at Racing NSW".

"I wanted to show support for Louise Herron's resistance to putting gambling advertising on our city and state's most recognisable landmark," petition organiser Mike Woodcock wrote.

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The son of Peter Hall, the architect who oversaw the completion of the opera House, described the plan as a "desecration".

"My father would have been sickened by it ... he would not have condoned advertising on the building in any way, lucky he's not around to see the desecration of our beautiful iconic masterpiece," Willy Hall told Fairfax Media.

Alan Jones defends interview

Alan Jones has denied claims he bullied Opera House boss Louise Herron during a testy on-air confrontation over the planned promotion.

The top-rating radio host on Friday attacked Ms Herron and repeatedly told her she should be sacked after she ruled out allowing words or branding highlighting The Everest race to be projected onto the Opera House because "it's not a billboard".

AAP

"Who do you think you are," Jones repeatedly asked Ms Herron. "You don't own the Opera House ... I'm telling you I will be speaking to (NSW Premier) Gladys Berejiklian in about five to three minutes and if you can't come to the party you should lose your job."

Jones on Monday said Ms Herron had been going on with "nonsense" about the Opera House's heritage when he wanted an answer.

"Yes, I did say I believed her job should be on the line. She might have been representing some people but not the wider public," he said on radio 2GB.

He denied telling the premier to get rid of Ms Herron, who currently retains her position as chief executive.

Additional reporting by AAP.