"I thought you might like to hear a man's voice," Senator Barry O'Sullivan's voice boomed during a fiery Senate estimates hearing on Tuesday morning.

This was to set the tone of the day's hearing where there was a much more aggressive edge to the Main Committee Room in Canberra than the day before.

The Coalition government was eager to assert itself as it finally got to take on the Australian Human Rights Commission president, Professor Gillian Triggs.

While Immigration Department secretary Michael Pezzullo had been free to refer the senators' many questions to his colleagues sitting beside him on Monday, this concession did not always apply to Professor Triggs.

"My question is for Professor Triggs," Senator O'Sullivan said, refusing to hear from her relevant colleagues. "No, I'm sorry, Ms [Julie] O'Brien, this is the question for Professor Triggs," he said. "I'm interested in the Professor's answers," he would repeat.

But the attacks didn't stop at the embattled president of the commission.

Female senators were also being barked at by Senator O'Sullivan and the committee's chairman, Senator Ian MacDonald.

When Labor senator Penny Wong accused Senator O'Sullivan of bullying and berating Professor Triggs, he shot back: "Oh dear, oh dear, Penny, settle down."

Later, Senator Wong accidentally began referring to the Attorney-General's Department's secretary, Chris Moraitis, as "Mr Moriarty". After apologising, she blamed it on reading too much Conan Doyle.

Senator MacDonald replied: "I am glad I did not say that. I would have been accused of other things, but anyhow, carry on."

"Reading the classics?" Senator Wong asked.

"You might have been accused of sexism, Senator Macdonald," Senator Brandis quipped.

"How is reading Conan Doyle sexist?" Senator Wong replied.

But only hours before the day, had begun with an apology.

Senator MacDonald said his office had been contacted by a voter who accused him of bullying Greens senator Sarah Hanson-Young during estimates on Monday.

By the afternoon, he was telling Professor Triggs how he wanted her to answer the question.

"This is what I want you to do," he instructed. "I want you to speak in first person, you're talking about it in the third person."

Women could be heard quietly gasping in the audience.

"You might talk to your wife like that but not to senators," Sarah Hanson-Young schooled Senator MacDonald.

Professor Triggs, sitting two seats across from Senator Brandis during the grilling, maintained a solid front throughout.

While admitting she was "certainly very shaken and shocked" by the meeting earlier this month in which she was asked to resign, she said on Tuesday the offer from Senator Brandis's office to shift her out to a different government job was a "disgraceful proposition".