Under cross-examination on Friday, Mr Parker said "I can't recall" at least 28 times within an hour in response to questions put to him.

Mr Parker said he was in Canberra on July 29 last year when the documents were delivered to his Lidcombe office by Cbus official Lisa Zanatta, who was recently sacked after she was caught lying to the royal commission on trade unions about her involvement in leaking the documents.

During cross-examination on Friday, Mr Parker said that he had spoken to Ms Zanatta eight or nine times from July 18, including on July 30, the day after she flew to Sydney from Melbourne and delivered the documents to his office in Lidcombe.

Mr Parker, who is secretary of the NSW branch of the CFMEU, said he had not seen the documents delivered to his office until they were presented to him by lawyers.

"I have never put my eye across those documents," Mr Parker said.

Counsel assisting, Jeremy Stoljar, SC, said: "If documents are delivered to your office and the receptionist is asked to give them to you, in the ordinary course of practice they're given to you – that's right, isn't it?"

Mr Parker said: "Well, if that's the normal practice, yes. They would ... the receptionist would drop the documents to me if she was told to drop them to me."

When Mr Stoljar put it to Mr Parker that he and Ms Zanatta had "concocted a plan pursuant to which she obtained this material from Cbus including contact details [and] brought it to Sydney," Mr Parker replied: "Absolutely not."

Mr Parker denied having said to former union official Brian Fitzpatrick: "We have to be very careful we don't tell anyone about it. If this comes out, I'm dead. The girls are dead and they'll be sacked and I'll be sacked."

He also denied the "girls" he allegedly spoke of were Ms Zanatta and her former colleague Maria Butera. And he denied having any knowledge of confidential information about members being disseminated to other CFMEU branches, including Queensland, or to CFMEU lawyer Tom Roberts.

During his previous appearance before the royal commission on October 3, phone taps were played in which Mr Parker was heard calling a union official a dog and spoke of wanting to bash him after the official raised concerns about the union's dealings with underworld figure George Alex.

The tapes were played after Mr Parker denied having ever made such comments.

Ms Zanatta admitted to deliberately giving false evidence to the royal commission to protect Mr Parker, "Cbus and the CEO".

The chief executive of Cbus, David Atkin, told the royal commission on Thursday that he understood her to mean that in protecting him, she was trying to protect the reputation of the fund.

"Clearly the fund has been very damaged by the revelations, completely unacceptable, and I've taken her answer in that context [to mean] the reputation of the fund has now been raised into question," he said.

Mr Atkin said Ms Zanatta's employment had been "terminated" and that his organisation had "cultural" problems that needed to be addressed.

When Mr Stoljar asked Mr Atkin whether he took responsibility for the culture of Cbus, he said: "Ultimately as the CEO, I must."

During her appearance before the commission on October 3, Ms Zanatta was forced to admit to lying about her role in leaking confidential information about members after commissioner Dyson Heydon warned her about the criminal penalties for giving false evidence.

The commission revealed credit card records and a taxi GPS trace showed Ms Zanatta had caught a taxi to Mr Parker's Lidcombe office after she said that she had attended an inner-city venue instead.

When it became clear the records contradicted her version of events, she admitted to having lied.

Cbus manages $27 billion of members' funds.

The hearing will continue at a date to be set.