Victoria Police have also announced they will likely issue infringements to the protest organisers if the event goes ahead in breach of COVID-19 social distancing rules.
NSW Police will apply for an injunction from the Supreme Court to stop Saturday's Black Lives Matter protests going ahead, arguing it breaches public health orders.
The announcement came as Victoria's deputy police commissioner Shane Patton confirmed organisers of the Melbourne event could be fined under COVID-19 social distancing rules if more than 20 people attend.
More than 17,000 have clicked 'attending' on the Facebook event for the Melbourne protest, and a further 10,000 in Sydney.
NSW Premier Gladys Berejiklian told reporters on Friday that approval was given earlier in the week for what the government thought would be a small gathering.
With thousands now indicating they will attend the rally starting at Sydney's Town Hall, Ms Berejiklian said protesters could not guarantee that social distancing requirements could be met.
"The NSW Government would never ever give the green light to thousands of people flagrantly disregarding the health orders," she said.
Victorian Premier Daniel Andrews urged people not to attend the protest in Melbourne because it was "not safe", with social distancing rules in the state barring gatherings of more than 20 people.
"My advice to all Victorians is: don't go," he said. "That is my appeal to Victorians."
During the same media conference, Deputy Commissioner Patton said the police force had been working with organisers and calling on them to cancel the event.
"If it goes ahead, we will probably be having to apply a lot of discretion because you can't practically issue thousands and thousands of infringements to people who gather in a large protest," he said.
"We will today be notifying [the organisers] that if this goes ahead, and the protest breaches the chief health officer restrictions, they will be getting infringements in all likelihood for the offence."
Protests against police brutality and Indigenous deaths in custody are also planned in Brisbane, Adelaide, and Perth on Saturday. Hundreds of people gathered at a peaceful protest in Canberra on Friday, but no infringements were issued.
Intense protests have swept the world after an unarmed black man, George Floyd, was killed at the hands of police in Minneapolis on 25 May.
The family of David Dungay Jr, a 26-year-old Dunghutti man who died in Long Bay jail in 2015 after stating "I can't breathe" 12 times, address ed the media after Ms Berejiklian's announcement.
Mr Dungay Jr's mother, Leetona Dungay, said she was going to march on Saturday "whether they like it or not".
"Black lives matter and we are not going to stop, we are going to march. We don't care what an act of law says, because those acts of law are killing us," she said.
"I'm marching for my son, and nothing is stopping me."
One of the Sydney protest organisers, Faith Black from the Indigenous Social Justice Association, called on Australians to "work together" to end Indigenous deaths in custody.
"We want people to look at us, hear us, and stand with us," she said. "We want to work with you, and we expect that in return."
The legal challenge comes after Prime Minister Scott Morrison urged people not to go to the protests, noting that people had commemorated Anzac Day by standing on their driveways rather than attending ceremonies.
"We found a way to celebrate those who gave us our liberty. Let's not misuse that liberty, let's respect it, let's respect other Australians," he said.
"All Australians owe all those other Australians a great duty of responsibility, and I say to them: 'Don't go'."
Earlier on Friday, NSW Police Minister David Elliot said anyone planning to protest was "certifiably insane".
Ms Berejiklian said many people had made sacrifices to limit the spread of coronavirus.
"If people had made the decision to express their views strongly in a COVID-safe way, which is the comments we made yesterday and the comments the day before, that would have been acceptable within the health orders but that is not the case," she said.
The South Australian police commissioner has granted permission for the Black Lives Matter protest to proceed in Adelaide.
Up to 4,000 people are expected to gather in Victoria Square on Saturday before marching through the city.
Commissioner Grant Stevens said the exemption will allow the event to go without breaching COVID-19 restrictions but those taking part must still be mindful of their own health and the health of others.
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