The Australian reporter Liam Mendes had attempted to question Mr Costello at Canberra Airport on Thursday over allegations of harassment at Nine, and a video of the interaction appears to show the former Liberal treasurer knocking the journalist over.
Labor Treasurer Jim Chalmers took aim at Mr Costello over the incident.
"I think it's really important that we treat journalists with respect, that journalists are safe in their workplace. And if anyone should know that, it should be the chairman of a major media organisation," Dr Chalmers said.
"It's for the people involved in it to explain what has happened there. It's a matter for the journalist whether or not that's taken any further."
EXCLUSIVE: Nine chairman Peter Costello has pushed a journalist to the ground at Canberra Airport, after refusing to answer questions on the rolling harassment scandal at his media company: — The Australian (@australian) https://t.co/NtoeGBEL3P pic.twitter.com/5WTyK2TP8eJune 6, 2024
Mr Costello said he did not assault the journalist.
"I walked past him, he walked back into an advertising placard and he fell over," he told reporters later on Thursday.
"I did not strike him.
"If he's upset about that, I'm sorry, but I did not strike him."
In a video published by The Australian, Mendes follows Mr Costello through the airport as he asks about Nine chief executive Mike Sneesby.
Mr Costello appears to walk towards the reporter at one point before the journalist falls backwards.
"You have just assaulted me," Mendes says in the video.
No complaint has been lodged with police over the incident.
The Australian reporter Liam Mendes was attempting to question Peter Costello. (Joel Carrett/AAP PHOTOS)
Canberra Airport has been contacted for comment.
The Nine boss was appointed in 2016 after a career in politics where he served as the federal treasurer under Liberal prime minister John Howard.
Nine's board met in Sydney on Friday morning over a separate issue, but the agenda was updated to include the incident involving Mr Costello.
Deputy Liberal leader Sussan Ley labelled it an "untidy incident" and called for respect to be maintained.
Good Talent Media chief executive Tony Nicholls said Mr Costello was likely under pressure at the time it happened.
"But whether it was stress, adrenaline, lack of coffee or simply a brain fade, the consequences are clear and the behaviour was unacceptable," Mr Nicholls said.
Mr Costello may have acted on "the secret fantasy of so many high-profile people" in the confrontation, he said.
"But the lesson is pretty clear here: if your instinct is to knock a reporter out, save it for your fantasies."
Peter Costello served as the federal treasurer under John Howard. (Bianca De Marchi/AAP PHOTOS)
Education Minister Jason Clare said it was a matter for police but everyone should be safe at work.
"My view is that if a journalist asks you a question, you stop and answer it," he told Seven's Sunrise program on Friday.
"That's the simplest way to do it, rather than run away or say 'no comment' or accidentally knock somebody over."
Opposition Leader Peter Dutton said he hoped Mendes was OK.
"I've never known Peter to be aggressive or anything of that nature," he told reporters.
"You see the enthusiasm of journalists, and they're multi-skilled ... some of them with good skills, some with bad skills, depending on which organisation you're coming from.
"Sometimes when they're walking backwards, some have the ability to stay upright, others don't."
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