"We respect each other and neither of us will be commenting further."
The pair were childhood friends and Mr Gyngell was the best man at Mr Packer's glittering wedding on the French Riviera to model Erica Baxter in 2007.
Bondi resident Chris Walker, who claims to have witnessed the incident, tweeted about a "massive street fight" outside the home on Sunday afternoon.
He later described the fight on his Facebook page.
"Holy crap, big street fight outside my house ... Not thugs, James Packer ... And some other angry bloke going toe-to-toe - total brawl ... Wow.
"Packer packed a punch but copped a couple of hits straight to the jaw ... Then they all fell on the concrete fence and I think the other guy broke his face ... They were looking for teeth after he left,' Walker said on Twitter.
A witness told Network Ten he heard Mr Gyngell yelling on a phone that he was waiting for Mr Packer, who arrived home soon after.
No words were exchanged as the two "went at it hammer and tongs", Ten said, citing the witness.
The fight had to be broken-up by Mr Packer's security guards and a limo driver.
Seven Network reporter Chris Reason tweeted that he had seen the pictures.
"They are extraordinary. Gyngell bearded and barefoot, Packer black eye, both in head locks on ground," he said.
The relationship between the two is said to have soured after Mr Packer announced his separation from Ms Baxter six months ago.
The incident also comes just days after model Miranda Kerr, with whom Mr Packer has been rumoured to be romantically involved, returned to Australia on a promotional visit.
Other media reports suggest Mr Packer believed a Nine Network satellite news van had been parked outside his house.
-AAP