Labor has accused Mr Brough of misleading parliament over an interview he gave on the Nine Network's 60 minutes program about the controversy surrounding the diaries of ex-Speaker Peter Slipper.
Mal Brough has offered a partial apology.
Labor has piled pressure on the Special Minister of State, Mal Brough, arguing he misled the parliament.
The opposition also demanded Prime Minister Malcolm Turnbull sack his Liberal frontbencher over the controversy.
Labor's legal affairs spokesman Mark Dreyfus put a censure motion against Mr Brough, seconded by Labor frontbencher Tony Burke who also challenged the Leader of the House, Christopher Pyne, to defend the minister.
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But the government used its numbers to cut short any debate by gagging Mr Dreyfus and Mr Burke.
Mr Dreyfus argues Mr Brough should not have been appointed as a minister in the first place, and should now stand aside.
"Since of course, he was appointed, there's been the extraordinary circumstance of the Australian Federal Police executing a search warrant on the home of a serving minister. I can't remember the last time that occurred and that alone should be sufficient for him to be stood aside by the Prime Minister if he won't stand aside himself until that police investigation is completed."
Mr Dreyfus says Mr Turnbull displayed atrocious judgement in appointing Mr Brough to a ministry and claims the role was a reward for Mr Brough.
"Whatever one can say about Mal Brough... He's clearly good at plotting and this was a reward from Malcolm Turnbull to him for Mal Brough's role as yet undisclosed in the plotting that took place over the course of this year to remove Tony Abbott as prime minister of Australia."
Yesterday Mr Brough suggested the 60 Minutes program misrepresented him.
He says the network selectively edited a TV interview to show him admitting asking former staffer James Ashby to obtain copies of his former boss Peter Slipper's diary.
However, the Nine Network soon released the raw footage of the interview showing journalist Liz Hayes verbally stumbling at the start of the disputed question, but still making it clear what she was asking.
Deputy Labor Leader Tanya Plibersek has told the ABC Mr Brough clearly misled parliament when he suggested the interview was not a fair representation.
She said the Prime Minister has no choice but to stand Mr Brough aside.
"It's up to the prime minister really, to answer the question. Here's the Minister who's responsible for enforcing the rules in Parliament, the rules around integrity. Is he the right person for the job?"
But Liberal MP Philip Ruddock has defended his colleague.
"I don't comment on the specifics of any of those matters. They'll pan out as they will. But there are appropriate standards and I am sure all of my colleagues recognise that if there is a necessity, it would have evolved that way but I think we're still to make the judgements on that."
He says he's satisfied with Mr Brough's explanation.
James Ashby is the former Liberal staffer who worked for Peter Slipper.
He's rejected claims that Mal Brough asked him to obtain copies of the ex-Speaker's diaries.
Mr Ashby told radio 2GB he was never asked to do it, despite what Mr Brough said in parliament yesterday.
"Let's save some taxpayers' money because this has cost millions already. There is no case to answer for because Brough never did it. I want to make it real clear. This was a whistleblower's case and it should have been treated like that. If I was a female, this would never of happened."
Special Minister of State Mal Brough, meanwhile, has given a partial apology to parliament.
"Mr Speaker, my recollection of the interview was that the question was put to me in a somewhat disjointed manner, and I answered the question without clarifying precisely what part of the question I was responding to. This is confirmed by the tape provided by 60 Minutes and that was the reason for my answer yesterday. Mr Speaker, I have taken the opporutnity to review the tape and transcript, and apologise to the House if my statement yesterday unwittingly added to the confusion rather than clarifying the matter."
Federal police have executed search warrants at Mr Brough's Queensland home as they continue to investigate whether the minister asked Mr Ashby to procure Mr Slipper's diaries.
The search warrant also mentions two other ministers, Wyatt Roy and Christopher Pyne.
