Immigration Minister Andrew Giles introduced the laws on Thursday, following the High Court decision last week which found indefinite detention was unlawful.
The laws, which will apply to the more than 80 detainees released since the High Court decision, will see new visa conditions imposed.
Andrew Giles says the safety of the Australian community is paramount.
The opposition had been pushing the government on the potential threat posed by criminals, including three murderers and a number of sex offenders, who were released into the community.
Opposition Leader Peter Dutton supported the laws in the lower house, but said the measures were too little, too late from the government.
Mr Giles said community safety was paramount.
"The government is working to ensure the individuals are managed appropriately under the relevant legal frameworks," he told parliament.
Liberal senator James Paterson said it should have been introduced to the Senate last week.
He criticised Mr Albanese for dodging responsibility by jetting off overseas "while criminals remain free to roam the streets".
The coalition will be putting forward amendments.
Penny Wong urged the opposition to stop "playing politics" and support the government in getting the legislation through as soon as possible to keep Australians safe.
Greens immigration spokesman Nick McKim said the "draconian laws" would provide the minister with powers never before seen in Australia.
"It is an utter disgrace, an abject craven capitulation by a party (Labor) that has forgotten where it has come from, and forgotten what it used to stand for," he said.
Greens Senator Nick McKim described the fast-tracked laws as "draconian".
The laws would create a two-tiered justice system for some migrants and refugees in comparison to Australians, he said.
The immigration minister said the measures such as electronic monitoring and curfews would not apply to all of the former detainees and assessments would be carried out to identify those at the greatest risk of reoffending.
"These measures are consistent with the legitimate objective of community safety and the rights and interests of the public," Mr Giles said.
New visa requirements for the released detainees will force them to notify the government on a change of address, or any association with clubs or organisation or individuals involved in illegal activity.
Each breach of the new visa conditions would carry with it a maximum penalty of five years in prison.
The government indicated it was considering further safeguards.
Mr Dutton said community safety was put at risk by the release of the detainees following the court's decisions.
"These are people who have committed serious offences and the likelihood of them reoffending is very, very high."
Home Affairs Minister Clare O'Neil said the laws were urgently needed.
"People at the heart of this decision have committed horrible crimes, disgusting crimes, crimes that no one in this parliament surely would accept, that is why we kept them in detention," she said.
"We are going as far as we can in order to manage the issues that are before us."
Greens leader Adam Bandt, along with fellow party members Stephen Bates and Elizabeth Watson-Brown, were the only MPs to vote against the laws.
Refugee Legal executive director David Manne said the planned measures were disproportionate.
Many of those released after the court decision had already served their sentences and ordinarily would have been released into the community.
Instead, they had been funnelled straight into indefinite immigration detention.
The Australian Federal Police commissioner this week briefed his state and territory counterparts about the court's decision and a joint operation with the Australian Border Force has been established to co-ordinate the release of the detainees.
The High Court is yet to release the reasoning for its decision.
