The High Court forced the government to release 80 immigrants in detention after ruling their indefinite detention - with no other country willing to take them - was illegal.
Serious offenders who have been released have had strict visa conditions imposed, including checking in with police officers and restricted employment options.
Home Affairs Minister Clare O'Neil said the conditions were "the strictest possible that are available under Australian law".
"Some of these people have committed disgusting crimes," she told parliament on Tuesday.
"Some of them have hurt people who are still here in our country and it is those victims that we care about."
The Australian Federal Police commissioner has briefed his state and territory counterparts about the decision and a joint operation with the Australian Border Force has been established to co-ordinate their release.
The opposition has seized on the release of the offenders, peppering the immigration minister in parliament about whether taxpayers' money was being used to house them upon their release.
Immigration Minister Andrew Giles reiterated that the Commonwealth government opposed the release and the High Court ruled against it.
Mr Giles said money was being spent to ensure the continued monitoring of where certain offenders were staying after their release.
'Our concern is to maintain community safety, a critical element of that in some cases is having some control over where an individual lives," he said.
Opposition Leader Peter Dutton accused the minister of not being prepared for the decision.
"If there was another option available – which I honestly believe that there is – then they could have prevented these people from getting out onto the streets," he told Sydney radio 2GB.
Mr Giles said the government had continued to look at "all regulatory and legislative options", but was hamstrung in its response as the High Court's reasons for the decision had not yet been published.
The government sought prior advice about options depending on a variety of outcomes of the court's decision, he added.
Mr Dutton said the minister needed to do "everything within the law to make sure that you can stop these people from getting back out onto the streets".
Attorney-General Mark Dreyfus added that the government had to act in accordance with the ruling.
"When the High Court finds that individuals are being unlawfully detained, the government cannot ignore it because ... the government must act in accordance with the law," he said.
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