Federal Labor has blasted Greens MP Max Chandler-Mather after his fiery speech to 4000 striking construction workers in Brisbane.

The Brisbane MP slammed the administration process for the CFMEU at one of several rallies across the country that drew tens of thousands of workers.

On Wednesday, Workplace Relations Minister Murray Watt said it was “very, very disturbing” that Chandler-Mather had been prepared to appear at a rally that featured banners labelling Prime Minister Anthony Albanese a Nazi and likening him to Adolf Hitler.

“When you share a stage with a group, you make a choice, and you’re endorsing the culture and behaviour of that organisation,” he told ABC radio.

“That’s exactly what Greens MP Max Chandler-Mather did yesterday.”

Watt condemned banners scrawled with “Alba-nazi” and depicting the PM as Hitler. He said he also saw a coffin being carried in the crowd with Albanese’s face on it.

“What does it say to people that a Greens MP puts grandstanding in front of a crowd above making a statement about what’s respectful or not?” he said.

Posters of Anthony Albanese and ACTU secretary Sally McManus at the Brisbane march. Photo: AAP

Finance Minister Katy Gallagher also accused the first-term Greens MP of grandstanding.

“We know he’s never seen a stage he doesn’t want to jump on,” she said.

“He really needs to explain why he thought it was appropriate to speak at that rally, particularly with such serious allegations of violence, intimidation and misogyny.”

But Chandler-Mather said the government had used “untested allegations to attack an entire union”, setting a dangerous precedent to seize control of a civil movement or other unions.

He linked his support to the principle of a fair trial, adding “the Greens strongly oppose any misogyny, intimidation or thuggery and any allegations of wrongdoing”.

“We live in a country that is not trial by media, it’s … fair process with the presumption of innocence,” he told the ABC’s 7.30 program on Tuesday night.

On Wednesday, Chandler-Mather defended appearing at the march.

“Of course, I don’t agree with those signs, they’re offensive. However, it’s ridiculous to expect a speaker to audit every sign that appears at a rally with thousands of people in attendance,” he told the ABC.

Greens leader Adam Bandt said the event was “legitimate” despite the posters.

“The sign is offensive. That’s not a sign that we did or shared or anything like that, it’s a sign that someone had at a rally, but it’s offensive,” he said.

Up to 50,000 workers marched in Melbourne and thousands more turned out in Sydney, Brisbane and other capitals on Tuesday to protest the action against the CFMEU, despite threats their pay could be docked if they took unprotected action.

Watt, who oversaw the ushering in of laws to put the CFMEU’s construction division into administration, said the broader labour movement supported what the government did.

The vast majority of marchers were CFMEU members supported by “a couple of other construction-related industries, plus other divisions of the CFMEU in the case of the Maritime Union”.

But most unions and their members didn’t attend the rallies, Watt said.

“That’s because they recognise the damage that has been done to the union movement,” he said.

Union leaders across the country have chastised Labor and branded the party, which has its roots in the labour movement, as traitors.

The Electrical Trades Union plans to withhold $1 million from Labor ahead of the federal election. It will use the funds to back a legal challenge against the administration.

Watt said the laws were set up to withstand such a challenge and questioned whether other unions would put their money where their mouth was to back the challenge.

“People make comments in the heat of the moment … let’s wait and see what actually happens and what legal challenges actually get funded,” he said.

“I would encourage them to also reflect on the massive gains that have been delivered to their members by this Labor government.”

Asked about the effect on Labor’s election war chest, Gallagher said it wasn’t about the donations for the party but about “what’s the right response to serious allegations about violence, intimidation and misogyny in a union”.

The Greens’ refusal to back the administration laws or rule out receiving donations from the CFMEU has sparked anger within the government as the minor party targets Labor seats.

Ousted CFMEU national secretary Zach Smith said the union was here to stay and outlined key policies in “the best interests” of members including on Palestine, housing and taxation.

All three issues overlap key tenets of the Greens’ platform.

-with AAP