The maverick politician sparked outrage after threatening to punch a TV reporter when asked about his Lebanese heritage at a press conference.
Prime Minister Anthony Albanese on Friday weighed in, telling the 80-year-old federal MP to take "a look at himself".
Queensland state MP Robbie Katter defended his father, saying the question about their family history had touched a nerve.
However he was reluctant to go into detail about the matter that had apparently triggered his father when he spoke to AAP on Friday.
"Knowing him and some of his personal background, I'm quite confident there are some very deep personal issues that the journalist in question has tapped into," he said.
"He's touched on a very deeply personal touch point with him, of which we tried to warn him to divert that line and he chose not to."
Mr Katter was flanked by his son and two other Katter's Australian Party colleagues at the press conference in Brisbane on Thursday when he became irate.
His grandfather Carl Robert Katter immigrated from Lebanon to Australia in 1898.
But Mr Katter - known as parliament's Father of the House - lost his cool when asked about his Lebanese heritage by Nine Network journalist Josh Bavas.
"Don't say that, because that irritates me, and I punch blokes in the mouth for saying that," he yelled, cutting off the reporter's question.
"I am Australian. My family have been here since the dawn of time."
He then approached Bavas with a raised fist when the reporter tried to ask a follow-up question.
"You're a racist," the independent MP for the Queensland seat of Kennedy said, holding his fist close to the reporter's face.
Bavas led calls for Mr Katter to apologise for his "unacceptable" behaviour, with federal MPs weighing in on Friday.
Robbie Katter said he had not been in touch with his father since the press conference and was unsure whether an apology was forthcoming.
"I certainly don't feel like I owe him any apology, but I do wish him well," the third-generation politician said of Bavas.
"I think he's a good journalist and I don't think he necessarily had any malice intended."
Mr Albanese said Mr Katter - federal parliament's longest-serving MP after first winning his seat in 1993 - had to consider his actions.
"Look, Bob Katter I like. But Bob Katter needs to have a look at that footage," he told Nine Network's Today Show.
"Have a look at himself, frankly, and recognise that that's just not what we expect of any Australian, let alone someone who's in public office."
Nationals leader David Littleproud said Mr Katter's behaviour was not becoming of a federal MP.
"It doesn't matter who you are or how iconic you think you are," he told ABC Radio National on Friday.
"Bob wears the big hat and it all seems all great ... but I don't think that sort of behaviour is appropriate for a federal member of parliament."
Asked if Mr Katter should apologise, Mr Littleproud said: "I'd like him to but I doubt he will."
Federal Health Minister Mark Butler said the Queensland MP was known for his quirky behaviour but crossed the line at the press conference.
"That is completely unacceptable," he told Seven Network's Sunrise program.
The Nine Network has backed Bavas, demanding the MP apologise for his display.
"His baseless and offensive accusation of racism is an irresponsible attempt to shut down a legitimate line of questioning," Nine Network's Fiona Dear said in a statement.
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