The minister is stripping at least 60 asylum seekers of their $200-a-fortnight welfare payments and government-supported housing.

Hundreds of others were "ripping the system off" in the same way.

Mr Dutton on Monday bemoaned "incredibly frustrating" constitutional challenges launched by lawyers representing those targeted in the crackdown.

"These lawyers have been playing the game with these people who are willing participants," he told Alan Jones on Sydney's 2GB radio.

"We're a generous nation, but we are not going to be taken for a ride."

Welfare payments were axed on Monday and the group will be evicted in three weeks after being shunted onto "final departure" bridging visas.

People who have come to Australia from offshore detention centres on Manus Island and Nauru for medical treatment are among those affected.

"The medical assistance has been provided and there is no need for them to remain in Australia and yet through these legal moves, they've found themselves a way," Mr Dutton said.

Natasha Blucher from the Asylum Seeker Resource Centre said the government's announcement had terrified people trying to rebuild their lives after enduring unimaginable suffering.

"It's cruel. It's impossible. It will end with children homeless. The only reasonable and compassionate thing to do is let them stay," she said.

The minister was asked whether he could pass laws forcing people to leave after receiving medical care.

"There's constitutional issues involved and, as you well know, we can't pass legislation to dispense with that difficulty of the constitutional issues," he said.

"So we defend these matters. We fight them in the courts and it is incredibly frustrating."

Jones asked Mr Dutton whether he agreed the lawyers' behaviour was "un-Australian".

"Of course it is, and it's gone on for too long," the minister said.

Law Council of Australia president Fiona McLeod said the extraordinary remarks broke with a long history of politicians showing respect for the legal system's independence.

"It is true that the legal rights of individuals can be an inconvenience to government, so attacking the legal professionals who work pro bono to defend those rights is truly extraordinary," Ms McLeod said.

"There is nothing more Australian than ensuring people are subject to the rule of law and have their legal rights protected."

Labor and the Greens will look to overturn the government's decision, which Bill Shorten has described as Malcolm Turnbull's "weakest move yet".

"I say to you Malcolm, we want these people resettled in third-party nations, we want to see the US deal come off, we don't want to see people smugglers back in business," the opposition leader told reporters in Melbourne.

"But do you really have to make a hero of yourself by mistreating in a weak and cowardly and cruel fashion the most vulnerable people in the world?"