Human rights boss Gillian Triggs has rejected Tony Abbott’s suggestions she might have instigated talk of an alternative role after the government lost confidence in her.

Federal police are examining whether Prof Triggs was offered an inducement to resign from her role as president of the nation’s human rights commission.

Mr Abbott and Attorney-General George Brandis said they had no confidence in Prof Triggs, following her report into children in detention which the PM described as a “political stitch-up” designed to embarrass his Coalition Government.

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Labor used question time on Thursday to quiz Mr Abbott and Foreign Minister Julie Bishop on the detail of a discussion between the secretary of the attorney-general’s department Chris Moraitis and Prof Triggs.

Ms Bishop told parliament no job offer was made to Prof Triggs, nor was she asked to resign or any inducement offered.

“A role was raised that related to international affairs,” Ms Bishop said.

“As the secretary of the attorney-general’s department said in Senate estimates, it was a sensitive matter that he did not wish to give details of in Senate estimates so I don’t give details of it.”

Asked about the difference between a job offer and a “role raised”, Mr Abbott told parliament: “There is a world of difference. It depends on who raised the issue of a role and no specific job offer was made.”

In a statement issued through her office, Prof Triggs said she “categorically denies any suggestion that the issue of a job offer and resignation came at her instigation”.

Shadow Attorney-General Mark Dreyfus asked Mr Abbott whether he would allow the release of notes of the meeting between Mr Moraitis and Prof Triggs to clear the air.

“They’re notes that belong to the gentleman that made them whom we have total trust and confidence in,” Mr Abbott said.

Labor failed in an attempt to censure the government over the attack on Prof Triggs.

“Every day there’s a new lie from the government,” Mr Dreyfus said.