Read the letter from Mark Dreyfus to the Australia Federal Police in full below.

Australian Federal Police have been asked to investigate whether a job offer to Gillian Triggs in exchange for her resignation as Australian Human Rights Commission president has broken the criminal code.

Professor Triggs claimed the government sought her resignation, but declined to describe it as an inducement.

Opposition legal affairs spokesman Mark Dreyfus has written to the federal police calling for an investigation.

In a letter supplied to SBS, Mr Dreyfus said the alleged offer – made during a meeting with the Attorney-General’s Department on February 3, 2015 – was part of an attempt to avoid political damage to the Coalition.

“The Attorney-General’s offer to an independent statutory officer of an inducement to resign her position was president, with the object of affecting the leadership of the AHRC to avoid political damage to the Abbott Government, may constitute corrupt and unlawful conduct,” he said.

“I request that the matter be investigated by the Australian Federal Police as a priority.”

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Mr Dreyfus said the no reason was given for the offer, but Professor Triggs “drew her ‘own conclusions’ that it was because the Prime Minister was unhappy with the AHRC’s report”.

“Professor Triggs says there was ‘no doubt in her mind’ that the request to resign and the offer of further work were ‘very clearly linked’,” he said.

A Senate estimates hearing on Tuesday heard Attorney-General's Department boss Chris Moraitis had made a job offer after conveying the minister's lack of confidence in Professor Triggs.

The allegations follow criticism of Professor Triggs and her Commission’s report into the detention of asylum seeker children.

Prime Minister Tony Abbott has previously labelled the inquiry and its Forgotten Children report a "political stitch-up" and a "blatantly partisan" exercise.

Mr Abbott’s claims have been backed by Immigration Minister Peter Dutton, who accused Mr Dreyfus of “playing politics” on the issue.

“If they're referring a claim off to the police that's fine - there's nothing in it,” he told ABC Radio.

The AFP confirmed it had received the referral, but could not comment further.

With AAP.