Immigration Minister Tony Burke on Thursday announced the scheme aimed at drawing down the roughly 77,000 unlawful non-citizens in Australia.
More of those people will now be placed in detention for a matter of weeks, Mr Burke said, although the government will encourage them and others to leave of their own accord.
Greens immigration spokesman David Shoebridge said the policy was comparable with President Donald Trump's move to use US Immigration and Customs Enforcement (ICE) to round up and detain overstayers.
"If you don't want your immigration changes to look like what Donald Trump does, don't contract with the same private multinational prison company to open detention centres in Australia, because that's what Labor has said they're doing," he told reporters on Friday.
Senator Shoebridge challenged Labor to reintroduce the rest of the pre-2015 visa programs, which largely limited migration detention to criminals, not visa over-stayers.
Labor should stop focusing on net migration figures and instead increase resources to process visa applications and speed up the appeals process, he said.
"Maybe we can have a parliament that bases its immigration policy on evidence and what has worked in the past, rather than ... something that Donald Trump has reheated in his microwave."
A report by the International Detention Coalition in 2015 found the Community Assistance Program pilot had a 93 per cent compliance rate and offered a significantly cheaper alternative to detention.
Australia's pre-2015 migration detention regime put children in a "horrific pipeline," former head of the Australian Human Rights Commission Gillian Triggs told AAP.
"There were 1100 children held in detention without education, for more than a year and longer for some, but detained indefinitely," Dr Triggs said, referencing a 2014 report published by the commission.
"Most of those children were severely mentally and physically ill ... the damage that was done to children and families is well documented, and probably unique globally."
The report helped spur significant reductions in number of migrant children detained in Australia.
In the intervening decade, indefinite detention without reasonable prospect of being returned to one's own country has been outlawed by a landmark 2023 High Court decision, but it's unclear how that might apply to this change.
Labor's plan would also involve hiring 100 new compliance officers and freeing up 250 beds, as well as potentially repurposing a 100-bed quarantine facility near Melbourne Airport used during the COVID-19 pandemic.
Ramping up removals - voluntary or forced - would help bring net overseas migration down from 292,100 to meet budget forecasts of 245,000 in 2026/27 and 225,000 each year thereafter.
Mr Burke described the proposed new system as "modest".
"When people overstay, they come into detention, you give them a bridging visa first, at the end of the bridging visa, they come into detention and then they leave," he told the ABC's 7.30 program on Thursday.
