Prime Minister Scott Morrison says he has heard the concerns of Liberal colleagues worried by the plight of asylum seeker children on Nauru.

Key points: Liberal MPs Russell Broadbent, Craig Laundy and Julia Banks are behind the call

Liberal MPs Russell Broadbent, Craig Laundy and Julia Banks are behind the call The ABC understands they proposed children with the most severe illnesses be given priority

The ABC understands they proposed children with the most severe illnesses be given priority Labor's pledged to make it easier for children on Nauru to get treatment in Australia

But he indicated that a "back door" through New Zealand would need to be closed before a resettlement offer from that country could be considered.

The PM's comments came after federal Liberal MPs demanded that refugee and asylum seeker children on Nauru be brought to Australia, amid growing warnings about their plight.

Doctors are increasingly worried about the mental and physical health of about 80 children who have been on the Pacific island for up to five years.

Mr Morrison said that passing legislation to guarantee anyone transferred to New Zealand could not travel on to Australia would need to occur as a first step.

"There is a bill still sitting in the Senate from 2016 that would close the back door from New Zealand to Australia, which is opposed by the Labor party and the Greens and the crossbench senators preventing that protection being put in place," he said.

"I would urge them to reconsider their position on that."

The ABC understands the Government plans to call for a vote this week on the legislation, which would prevent asylum seekers who arrived by boat after mid-2013 from applying for an Australian visa.

It is unclear if New Zealand would then have to pass legislation of its own to prevent its residents travelling to Australia.

Questioned on his contact with colleagues who have aired concerns, Mr Morrison said work was being done.

"I've been meeting with those colleagues, as have the relevant ministers," he said.

"We've been acting on these issues. We haven't been doing it by making public statements about it every day, but we always consider each and every case on its merits and in the interests of the child, and we will continue to do that."

Labor has indicated it remains opposed to the specific bill before the Senate, ahead of the foreshadowed vote later this week.

Labor's immigration spokesman Shayne Neumann pointed to a refugee deal brokered directly with the United States preventing refugees from returning to Australia as evidence it is not needed.

"The Liberals' lifetime ban legislation has nothing to do with third country resettlement options because the US deal is already underway," he said.

"If Malcolm Turnbull was able to negotiate conditions for the US deal to proceed, why is Scott Morrison incapable of negotiating similar conditions for the NZ deal?"

'Pragmatic solution' to get children off Nauru

Liberal MPs Russell Broadbent and Craig Laundy met with Scott Morrison last month. ( ABC News: Nick Haggarty )

Backbenchers Russell Broadbent and Craig Laundy last month asked Mr Morrison to evacuate all of the children and their families from Nauru.

The ABC understands the Government MPs proposed moving children with the most severe illnesses as a matter of priority, before transferring other children.

Liberal Member for Chisholm Julia Banks also thinks the situation on Nauru has reached a "tipping point" and the Australian Government should change its approach.

The MPs told Mr Morrison the public mood had shifted regarding Australia's offshore processing regime, and a pragmatic solution was needed.

A well-placed source said Mr Morrison told the MPs in the meeting he was working on a solution.

The MPs' intervention, first reported by News Corp Australia, increases pressure on the Morrison Government over the long-running issue.

There is growing concern about the deteriorating health of refugee and asylum seeker children on Nauru. ( Supplied: World Vision )

The asylum seekers would only be in Australia temporarily — in detention or in the community on bridging visas — before being resettled in another country, according to The Herald Sun.

MPs briefed on children who attempted suicide

The growing Liberal unease follows a concerted lobbying campaign by the Australian Medical Association (AMA), which has met with backbench MPs and told them about children's suicide attempts.

AMA paediatric representative Paul Bauert, who met with around 30 MPs last month, said he was "delighted" the three Liberals had urged the Prime Minister to take action.

"I just wish that more politicians who I have spoken to who have expressed concern about what's going on with these children would be as brave and stand up and say enough is enough," he told AM.

Dr Bauert is in Canberra again this week for more meetings with backbenchers, where he will detail the cases, brought to his attention over the weekend, of two Iranian children aged 12 and 14 who have stopped eating.

"The two children I'm talking about have attempted, have spoken of, and are determined to suicide and would do so if they had the energy," Dr Bauert said.

"The psychiatrist who looked after these children several weeks ago was concerned about putting the children on anti-depressants because there was the risk they would develop the strength and determination to get out of bed and commit suicide."

Labor working on its own Nauru plan

Sorry, this video has expired MSF Australia calls for the immediate evacuation of all asylum seekers and refugees on Nauru.

Federal Labor's leadership group last night pledged to make it easier for refugee and asylum seeker children on Nauru to be brought to Australia for medical treatment, if elected.

Shadow Cabinet endorsed a suite of measures, which will go before all Opposition MPs and Senators for approval today.

Doctors' advice would be given more weight in decision-making under the plan, and the Immigration Minister, not the Home Affairs Department, would make all decisions about medical transfers.

The Minister's decisions would have to be made public, and if doctor's advice was rejected, the Minister would need to consider another medical opinion.

"This won't start the boats, but it will help sick children," a Labor source said last night.

"This is about the children and the children only. Who would argue against this?"

The ALP source said the proposal would not allow children or their families to permanently settle in Australia.

The ABC understands the Opposition could try to implement the changes through a private members bill during this term of Parliament.

Dr Bauert said the children need to be taken off Nauru immediately and that Labor's solution was too little, too late.

In Parliament yesterday Mr Morrison defended the medical care provided in Nauru. ( AP: Jason Oxenham )

"I just do not think that's practical. I'm deeply concerned about the health of these children. We cannot play around with this any further," he said.

Nearly 6,000 doctors and medical students signed a petition that was delivered to Parliament House on Monday demanding the children be removed from the Pacific island because of serious mental and physical health concerns.

Medical charity Doctors Without Borders last week called for the immediate evacuation of all asylum seekers and refugees from the island.

"Five years of indefinite limbo has led to a radical deterioration of their mental health and wellbeing," the organisation's Australian executive director Paul McPhun said.

The Prime Minister yesterday said decisions about medical transfers were made on a case-by-case basis, and defended the medical care provided on Nauru, which is about 3,000 kilometres from the Australian mainland.

"There are 65 health professionals contracted by the Australian Government to provide health services on Nauru, and that includes 33 mental health professionals," Mr Morrison told Parliament.