The government used its numbers on Wednesday to block a Labor attempt to censure Malcolm Turnbull and force the resignation of Mr Brough.
On Tuesday, the minister suggested in parliament the 60 Minutes program selectively edited a TV interview in which he bluntly admitted asking former Speaker staffer James Ashby to obtain copies of his former boss Peter Slipper's diary.
"In relation to the 60 Minutes interview, what was put to air was not the full question," Mr Brough told parliament on Tuesday.
However, the Nine Network has released the raw footage of the interview which shows journalist Liz Hayes verbally stumbling at the start of the disputed question, but still making it clear what she was asking.
"Um why then also did you um assist, seek well, did you ask James Ashby to procure um copies of Peter Slipper's diary for for you?" Hayes asked.
Mr Brough replied: "Yes I did".
The minister told parliament on Wednesday in a brief statement that his recollection was the question had been put to him in a "somewhat disjointed manner".
"I answered the question without clarifying precisely what part of the question I was responding to," he said.
"I have taken the opportunity 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."
Labor frontbencher Anthony Albanese jumped to his feet to say it was an "extraordinary statement" from the minister.
"There was no apology to the house," he said.
"A misleading of the parliament is a very serious offence."
Foreign Minister Julie Bishop told reporters "due process" should be allowed to occur.
Shadow attorney-general Mark Dreyfus earlier sought to censure the prime minister for his "atrocious judgment" in appointing Mr Brough as a minister in September, and accused the minister of "slithering and sliding".
Mr Turnbull, who has been away from parliament attending two overseas summits, demonstrated a "complete and utter failure" to show leadership to stand aside Mr Brough under the ministerial code of conduct, Mr Dreyfus said.
"He has shown himself to be someone that cannot even answer a straight question," Mr Dreyfus said of the minister.
Federal police have executed search warrants at Mr Brough's Queensland home as they investigate whether the minister asked Mr Ashby to "procure" Mr Slipper's diaries.
The criminal offence carries a two-year jail term.
The search warrant also mentions two other ministers, Wyatt Roy and Christopher Pyne.
Mr Ashby on Tuesday said Mr Roy had advised him to copy the office diary, as the former staffer sought to build a sexual harassment case against Mr Slipper which eventually failed.
