Sydney: The Australian government’s woes deepened Wednesday after police said they were investigating claims a senior official broke the law by allegedly offering an inducement for the Human Rights Commission chief to resign.

The president of the government-funded commission, Gillian Triggs, has been under heavy fire from Tony Abbott’s conservative administration since releasing a report this month criticising the detention of asylum-seeker children.

The commission’s “Forgotten Children” report hit out at both sides of politics over the issue and called for a national inquiry.

Australia has long come under international pressure over the detention of asylum-seekers arriving by boat, particularly in offshore camps in the Pacific.

In its annual report released on Wednesday, Amnesty International described Australia’s offshore detention of asylum-seekers as “inhumane” and said it must do more to help tackle the worsening refugee crisis around the world.

In explosive parliamentary hearings on Tuesday, Triggs said the government sought her resignation through the secretary of the Attorney-General’s Department, Chris Moraitis, two weeks before her commission’s report was released and offered her another position.

She said she rejected the request.

Labor opposition attorney-general Mark Dreyfus claimed this could constitute corrupt and unlawful conduct and referred the matter to the Australian Federal Police, which said it was investigating.

“The police will evaluate this referral as per usual processes,” it said in a statement.

Moraitis denied the claims, saying he “never sought her resignation”, but confirmed the job offer.

Dreyfus said the allegations “raise real questions about whether or not there’s been a breach ... of the criminal law”.

“We’ve got criminal laws that prevent and guard against inducing, trying to affect commonwealth public officers in the performance of their duties,” he told the Australian Broadcasting Corporation.

Abbott dismissed the claims and repeated that his government had lost confidence in Triggs, a respected international lawyer.

“What [Triggs] does is a matter for her but as the secretary of the Attorney-General’s Department has made clear, she was not asked to resign and no inducement has been offered,” he told reporters Wednesday.

On Tuesday Abbott called the report a “political stitch-up” and said it should have released when the previous Labor government was in power since more children were held in detention at that time.

Opposition Labor leader Bill Shorten said the attacks on Triggs reflected “a new and shocking low” for the government.

“What I don’t understand is, rather than dealing with the issues in the report, what they have done is attack her character,” Shorten told parliament.

Abbott, who survived a leadership challenge this month from within his own Liberal party and has been on the back foot ever since, has strongly defended his government’s tough approach to dealing with boat people.

Communications Minister Malcolm Turnbull — seen as Abbott’s main leadership challenger — said the furore “misses the main point”, which was about the children being detained.

“Our policy has demonstrably resulted in children being taken out of detention so that’s what we should be focused on,” he said.