Northern Territory candidate Wayne Kurnoth in February posted a picture showing Mr Turnbull as an Islamic State executioner about to kill the ABC's Emma Alberici.

"I think he has been incredibly stupid. He's not running in a winnable spot but we've told him, I understand the party has told him, to take it down and apologise straight away," Mr Shorten told reporters in Melbourne.

Mr Kurnoth has also been caught posting a seemingly disparaging and derogatory comment about former federal MP Joanna Griggs back in 2015.

However, the opposition leader is refusing to cut his candidate adrift.

Instead, he switched focus to the Liberal candidate for McNamara, who was forced to apologise for posting an emoji referring to his wife Chloe Shorten as a pig.

"I've said this bloke is incredibly stupid. Has (Scott) Morrison said that the candidate is incredibly stupid, which she is?" Mr Shorten said.

"Has Morrison actually set a standard for his own candidates that he's setting for ours?"

"I understand this bloke shouldn't have said it. He's number four on the Senate ticket, not running in a marginal seat like McNamara, but that doesn't excuse it. Stupid conduct is stupid conduct."

Cautioning people against lecturing others on the topic, Mr Shorten also launched a spray at the minor parties.

"If you want to talk about quality control in political parties, have a look at the Palmer United Party, have a look at the One Nation Party, have a look at the Liberal Party."

Australian Associated Press