The clash between the pro-Palestinian and pro-Israel supporters broke out on Sunday morning at Bondi Beach.
Hundreds of pro-Palestine supporters were gathering on the beach on Father's Day for a paddle-out in support of the fathers of Gaza.
The gathering was organised by a Jewish-led pro-Palestine group, which called on local boardriders to participate in the "peaceful event".
A counter-protest, backed by the fringe Australian Jewish Association, was held at the same time.
"During the assembly, members from different groups became involved in a brawl, with police intervening," NSW Police said in a statement on Tuesday.
Amid concerns about community safety, local police were called in to manage the protests alongside the public order and riot squad.
Police on Tuesday released images of three men they believe may be able to assist with their inquiries.
Premier Chris Minns said he hopes police "throw the book at the people that started it".
"People come to Australia because ... we are largely free of political violence," he told reporters on Tuesday.
"That's not the case in other countries and places around the world. We don't want that on Sydney streets.
"You've got a right to protest, you don't have a right to assault someone."
The premier, who opposed a major rally over the Sydney Harbour Bridge in August, said he did not want iconic Sydney locations being "routinely disrupted by political protests".
But there was not much the government could do further to prevent them, he noted.
"We've pursued changes to the law in relation to landmarks, religious institutions, racial vilification - we've been widely criticised for it," Mr Minns said.
"It's not as straightforward as passing a bill this afternoon saying 'that's the end of protests on Bondi Beach', it's almost certain to be knocked over by the High Court."
Numerous rallies have been held across Sydney and the rest of the country since the latest conflict between Israel and the designated terrorist group Hamas erupted on October 7, 2023.
Hamas, which effectively controls Gaza, invaded the country's south and killed more than 1200 Israelis and took about 250 more hostage. Some of those hostages remain captive.
Almost 63,000 Palestinians in Gaza have since been killed in Israel's military response, according to local health authorities.
Hundreds of thousands more face catastrophic levels of food insecurity in the decimated territory, the UN says.
