A small group of far-right supporters gathered at a Melbourne beachside park on Australia Day, while thousands marched through city streets calling for the national day to be scrapped or rescheduled.
Protesters at Parliament House chanted "always was, always will be, Aboriginal land" before walking through the city.
Tarneen Onus-Williams, who was introducing speakers during the rally, shouted to the crowd "f... Australia" and "I hope it burns to the ground".
Flowers and artwork were stacked at the steps, alongside signs reading 'pay the rent' and a giant cardboard coffin daubed with 'colonisation'.
Protester Pauline Williams said she couldn't understand why it was an issue to change the date.
"If there's so many people that it offends, because it's the anniversary of the invasion, my question is, why not change it?"
Melbourne kindergarten teacher Lily Ames, holding a sign, said she believed in equal rights.
"It's really important that young people are aware of what happened and the reason why the government said 'sorry'," she told AAP.
After the rally left to weave its way through the city, a handful of right-wing protesters arrived at the steps wearing Australian flags, but departed without incident.
Right-wing groups including The True Blue Crew and United Patriots Front headed to a reserve at St Kilda for a "citizens barbecue".
"This ... is the only actual Australia Day celebration which is taking place. Everything else is 'invasion day'," organiser Blair Cottrell said of the event in a social media post.
"Don't get sucked in by the brainwashing that's coming from the political and mainstream media which is legitimising and promoting this invasion day nonsense."
Up to 50 people attended the gathering at the reserve, where a heavy police presence included mounted officers, but no arrests were reported.
Mr Cottrell says Australia respects Aboriginal people.
"They have always been part of Australia. This is just leftists trying to create a big divide in our country," he said of the anti-Australia Day movement.
With an alcohol ban across the foreshore, the right-wing supporters played cricket and chatted surrounded by a dozen Australian flags.
Labor Leader Bill Shorten was one of many to speak about the protests during the day.
"(It) doesn't matter if you're on the far right or the far left, Australia Day shouldn't be an idiot magnet for a few yobbos and idiots," he said.
It's a day of national reflection, but people had to understand the history of Australia and "take the good with the bad", he added.
Among the crowd at the city rally was Australian Greens leader Richard Di Natale and state Greens MP Lidia Thorpe, the first female Aboriginal elected to the Victorian parliament.
Senator Di Natale said there should be a conversation about choosing a new date for Australia Day.
"We need to have a process to acknowledge why January 26 is not that day and to come together as a nation to talk about our history, to understand it more, to finally heal and then to come together," he told reporters.
