William Yekrop,a South Sudanese man who was in immigration detention for 10 years,has also been released.

Immigration Minister Andrew Giles said on Tuesday the freed detainees were being supported by government payments and living on temporary visas that included strict reporting conditions,repeating the Albanese government’s message its priority was to keep people safe.

“Such conditions include restricting types of employment,requiring regular reporting to authorities,and requiring released detainees to report their personal detail including their social media profiles,which we are actively monitoring,” Giles said in a statement.

Giles said while the government had argued against the release of these people,it could not overturn the decision through parliament after the High Court found their detention was unconstitutional.

“The government is exploring further measures,including legislative and regulatory options,to ensure community safety as we work through the implications of the High Court’s decision,noting the court is yet to hand down its reasons,” he said.

During question time on Tuesday,Giles confirmed 81 of the 92 former detainees had been released,refusing to answer Opposition Leader Peter Dutton’s question about why some others had not.

He told parliament multiple murderers and sex offenders had been released. “I believe there are three murderers,there are several sex offenders,” he said.

Opposition immigration spokesman Dan Tehan asked Giles if “the Albanese Labor government is now paying welfare payments to the 81 hardcore criminals?”

Giles said the release of people from immigration detention had been conducted “under the policies that are longstanding under both sides of politics,that ensure both the supports that are available under[Status Resolution Support Services] but also all the reasons around community safety I’ve already articulated”.

The SRSS payment is made available to people unable to support themselves while they try to resolve their immigration status in Australia.

Those entitlements have previously included financial hardship aid of about $3600,a crisis cash payment of up to $1000,a basic household goods package cap of up to $9850,a living allowance that is 89 per cent of Newstart,currently set at $555 a fortnight,and a number of other payments.

A spokeswoman for Giles declined to comment on individual cases and payments.

Kuster’s lawyer,Alison Battisson of Human Rights for All,warned the Coalition against “whipping up fear” and said the former detainees who had been convicted of serious crimes were outliers.

“They should be supported where needed to reintegrate into the community and be left alone to quietly do that,” Battisson said.

with James Massola

Cut through the noise of federal politics with news,views and expert analysis from Jacqueline Maley. Subscribers can sign up to our weekly Inside Politics newsletterhere.