Home Affairs working to re-detain most serious offenders after High Court ruling

But opposition spokesperson for Home Affairs, Liberal senator James Paterson, criticised the government and public servants for failing to apply for any preventative detention orders in the two months since the government introduced emergency legislation in December.

The legislation allows the Home Affairs Minister Clare O'Neil to seek to re-detain individuals thought to pose an unacceptable risk to the community.

"From the moment that the government preventative detention legislation passed this parliament last year, we've been working towards putting together applications for the re-detention of the most serious offenders," Labor senator Murray Watt told the Senate estimates committee.

"And will keep working closely with state and territory law enforcement on these applications.

"... Senator Paterson, I'm sure you would share my view that in seeking these applications against some serious offenders we want to get it right, we don't want to be defeated in a court."

But Senator Paterson criticised the government for not acting quickly enough, after it was revealed that six of the 149 people released had since been charged for breaching their visa conditions, while 18 had been charged for state and territory offences.

A taskforce of 20 public servants within the department is gathering tens of thousands of documents containing information available about the individuals in the group in order to determine prospects for applications.

Reassured by Home Affairs secretary Stephanie Foster that "extraordinary progress" had been made, Senator Paterson remarked: "Doesn't feel like it because there's not a single application that's been made".

Ms Foster called the process of pulling together information - which could see up to 35,000 documents amassed per person - "extraordinary".

"There's an enormous resource and effort going into this and the team is well advanced in the process and we will prosecute this with every energy we have and we will get those applications in," she said.

"We just need to work through the process and get it right."

Data tabled in Senate estimates on Monday, in response to questions by Liberal senators James Paterson and Michaelia Cash, revealed offences the cohort had been convicted of, before they were indefinitely detained.

The Albanese government was forced to released the cohort from November last year, when the court ruling determined it was unlawful to detain a person in immigration indefinitely when there was no prospect of removing them from Australia in the foreseeable future.

Seven people among the 149 had been convicted of murder or attempted murder, 37 people were convicted of offences categorised as sexually based offending, including child sex offending, and 72 people were convicted of assault and violent offending, kidnapping, armed robbery.

Sixteen people were convicted of domestic violence and stalking, 13 were convicted of serious drug offending, and a small number - less than five - were convicted of people smuggling or other crimes of serious international concern.

A small number - less than five - were convicted of offences or of a "low level" or were not convicted of anything.

In response to the ruling, the government introduced emergency legislation, including visa conditions requiring members of the cohort to wear electronic monitoring devices, adhere to curfews and seek approval before entering a range of employment types, including those relating to vulnerable people and children.

Home Affairs has now revealed that 113 people have been required to wear ankle bracelets.

Across multiple agencies engaged to respond to the High Court ruling, the costs had exceeded $13 million.

The sum includes employee and supplier costs, for things such as monitoring released detainees and immigration policy, and extends across Home Affairs, the Australian Federal Police, Services Australia and the Attorney-General's Department.

Home Affairs officials, including secretary Stephanie Foster, will face questions over their advice on the NZYQ case later on Monday afternoon.