Prime Minister Scott Morrison says his government could try to ban the CFMEU, after the construction union's Victorian secretary posted a tweet showing his children holding an obscene sign directed at the building industry watchdog.
The tweet, sent on Father's Day by CMFEU Victorian secretary John Setka, shows the children holding a sign telling the Australian Building and Construction Commission (ABCC) to "go get f***ed".
"Go catch real criminals you cowards," Mr Setka tweeted.
It prompted a fiery response from the new Prime Minister, who suggested he would look at new legislation to further regulate the unions and potentially seek to ban the CFMEU.
"This is the straw that breaks the camel's back," Mr Morrison told Melbourne radio station 3AW.
"I mean these guys are already demonstrating their lawlessness, and their thuggery, and their brutality, their threats. This goes on all the time, as we know.
"But I'm looking very seriously at this, I'm not rushing anywhere on it."
Mr Morrison said it would be an issue new Jobs and Industrial Relations Minister Kelly O'Dwyer would investigate.
"John Setka is supposed to be the tough guy of the union movement, but uses his children to fight his fights," Ms O'Dwyer said.
"It is beyond the pale. I am disgusted that any father would use his children in such an obscene way to attack a regulator for doing their job.
"The ABCC performs a critical role in stopping thuggery, intimidation and corrupt behaviour on our construction sites and they deserve our support and thanks."
Mr Setka deleted the tweet after Mr Morrison's comments, and sent another saying he "shouldn't have included kids" in the earlier tweet.
Labor frontbencher Anthony Albanese rubbished Mr Morrison's comments, and suggested it was further evidence of the Coalition's anti-union bias.
"[The Coalition] had a royal commission at a considerable cost to the taxpayers of Australia," he said.
"That royal commission, of course, was all about trying to damage Labor and damage Bill Shorten in particular. It failed."
Mr Morrison's predecessor Malcolm Turnbull forced a double dissolution election over the reintroduction of the ABCC after it was abolished by Labor when it was in power.
The ABCC has refused to comment on the tweet, but it is understood the organisation's chief Stephen McBurney has offered to meet with Mr Setka.
No response has been received.
Morrison says there is precedent for banning unions
Mr Morrison cited the decision to deregister the militant Builders Labourers Federation (BLF) in the late 1980s as precedent.
"We got rid of the BLF under Bob Hawke, and that was done with bipartisan support," Mr Morrison said.
"And so the question is: Will the Labor party finally do something about militant unionism?"
The Royal Commission into Trade Union Governance and Corruption set out the process the Federal Government could use to have the union's registration cancelled to "combat the disease", but did not make a recommendation to follow through.
Instead, the royal commission's final report argued individual union officials were responsible for misconduct rather than the organisation's members.
"Any targeted action to combat the culture of the CFMEU should focus on the officials of the union," the report stated.
The CFMEU has been contacted for comment.