By Kat Wong, Jacob Shteyman and Dominic Giannini in Canberra

Australia has been urged to take the threat of far-right extremism seriously after nationalists marched alongside neo-Nazis at anti-immigration rallies.

Tens of thousands of people, dozens of dogs and at least one horse draped in Australian flags and paraphernalia joined the March For Australia rallies on Sunday in major cities including Sydney, Melbourne, Adelaide, Brisbane and Canberra.

Though the protests were widely condemned as racist and a “neo-Nazi con” across the political spectrum, politicians such as independent MP Bob Katter and One Nation senator Pauline Hanson spoke at some events.

Prime Minister Anthony Albanese maintained “diversity is a strength in modern Australia”.

“(It) provides us with incredible economic opportunity due to the diaspora and our connections with every country on the planet,” he told parliament on Monday.

But the Greens accused members of both major parties of paving the ideological path to the weekend’s rallies.

“Labor and Liberals for years have punched down on migrants and refugees,” Deputy Greens leader Mehreen Faruqi told the Senate.

“I do hope that this is a wake-up call for all of you to change course and do something about far-right extremism, which you have been ignoring.”

The minor party’s senators pointed to a Labor bill that would allow hundreds of former immigration detainees to be deported to Nauru, which the coalition has indicated it would support.

Prominent neo-Nazis gave speeches in Melbourne and Sydney, where NSW Police estimated 15,000 people attended.

Speakers and attendees were at pains to state they were not against immigrants and wanted the federal government to pause or slow the pace of immigration.

But in Sydney, one speaker sprouted a theory about “a clear global agenda to shame, beat down and replace people with Anglo-Celtic and European heritage”.

Multicultural Affairs Minister Anne Aly said people had legitimate concerns around the strains immigration was placing on housing and infrastructure.

The protests were clearly targeted at migrants from “countries that have brown people”, not white Western countries, Ms Aly said.

“It’s very clear from the conduct that was observed … that these marches were a con by the far right neo-Nazis to prey on some legitimate concerns around housing and around cost of living in order to propagate their anti-immigration, racist agenda,” she told ABC Radio on Monday.

“One of the very clear calls to action that was listed there was anti-Indian immigration.

“Now that, to me, is clearly racist when you target a specific ethnicity.”

Opposition Leader Sussan Ley claimed the weekend’s rallies were “attended by people of goodwill but hijacked by neo-Nazis spouting hate”.

“That can never be accepted,” she said.

There was some diversity of views within the coalition, with senator Jacinta Nampijinpa Price congratulating those who marched.

Before the protests, organisers frequently repeated a claim that 1500 migrants were entering Australia each day, based on Australian Bureau of Statistics overseas arrivals and departures data.

But the bureau has said the figures are not a reliable measure of migration or population change but rather represent self-declared traveller intentions.

Former Immigration Department deputy secretary Abul Rizvi said successive governments had failed to communicate their immigration plans to the public, leaving a void to be filled by conspiracy theories and “bizarre ideas”.

The crowd was generally well-behaved in Sydney, except for two men who were charged after an officer was assaulted during a brawl at a pub on the march route.

It was a different story in Melbourne, where violence erupted between anti-immigration marchers and anti-fascist and pro-Palestine protesters.

More than 100 Canberran counter-protesters chanted “fk off Nazis, fk off”, “go home white trash” and “immigrants are welcome here”.

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