The Australian public continues to focus on the plight of children in detention on Nauru, despite the coalition's efforts to turn attention away from the issue.
A new poll shows most Australians want the government to accept an offer from New Zealand to resettle the detainees on Nauru.
The YouGov Galaxy poll commissioned by News Corp Australia reveals 79 per cent of people want children and their families transferred off the island.
Prime Minister Scott Morrison has distanced himself from the deal since flagging it as a possibility ahead of the Wentworth by-election.
The draft laws of the deal place a lifetime ban on resettled asylum seekers being allowed to enter Australia, which Labor frontbencher Brendan O'Connor says is an "overreaction".
"But right now the lives of people hang in the balance and we need to get people out of that detention centre," he told Sky News on Sunday.
"And if that is the offer on the table then certainly Labor is going to seriously consider that."
Labor would consider "case-by-case" permanent resettling of asylum seekers who are in Australia for medical treatment, he added.
Greens leader Richard Di Natale has vowed to do all he can to ensure children on the island are brought to Australia for medical care.
Mr Morrison has said the move would result in more refugees attempting to reach the nation by boat, leading to additional children in detention.
"That is utter nonsense and they are the words of a man who is completely lacking in any compassion, any decency, any humanity," Senator Di Natale told the ABC on Sunday.
Both the coalition and Labor do not support a bill before parliament to bring detainees to Australia for urgent medical care, but the Greens would do what it could with crossbench support, he added.
Independent Tasmanian MP Andrew Wilkie says any solution should ensure separated families are reunited.
Three Liberal MPs - Russell Broadbent, Craig Laundy and Julia Banks - have called for Mr Morrison to get children off Nauru.
Mr Wilkie says such MPs should grow "a backbone" and cross the floor to vote against the coalition on asylum seekers.
On Saturday, more than 1000 people stopped traffic in the heart of Sydney while about 500 protesters in Melbourne rallied against the offshore detention centres.
Eleven children were removed from Nauru earlier this week, leaving 52 on the island. Refugee advocates say another four kids have since left the island.
Mr Morrison said about 30 people had been taken off Nauru over the past few weeks.
Crowds have rallied in Sydney and Melbourne urging the government to end offshore detention. (AAP)
