Victorian Premier Daniel Andrews has drawn support from advocacy groups after offering to provide housing, health, education and welfare services for 267 asylum seekers, including 37 Australian-born infants.
Doctors for Refugees spokeswoman Dr Barri Phatarfod told SBS World News ensuring families are incorporated into mainstream Australia is crucial.
"The best chance that we'll have that they'll [asylum seekers] have a normal life and become a productive member of the community is actually by early integration...so this is the best thing we can possibly do and I just hope that Premier Andrews message gets listened to".
New South Wales Premier Mike Bairds said he supported the call to house Australian-born asylum seeker children and their families, saying his state is "prepared to help".
"I recognise the humanitarian impulse behind [Mr Andrews'] letter to the Prime Minister," Mr Baird said in a statement.
NSW Opposition leader Luke Foley earlier on Saturday called for the NSW government to follow Victoria's lead.
Last week the High Court ruled offshore detention on Nauru and Manus Island was lawful, clearing the way for more than 250 asylum seekers to be sent to Nauru.
In a letter to Prime Minister Malcolm Turnbull, Mr Andrews asked him not to send refugee children to a "life of physical and emotional trauma" in offshore detention.
Mr Foley said that as Australia's premier and most populous state, NSW should make a similar offer.
"I call on Premier Mike Baird to add our voice to the many calling for Malcolm Turnbull to show compassion to these 267 people and let them stay," he said.
"Together we should all strive to do better as a nation and we can take an important step forward today."
Mr Baird praised Mr Andrews as a "good man" and recognised the humanitarian impulse behind his letter.
"The same impulse has driven us to work co-operatively with the Commonwealth to resettle an additional intake of refugees in NSW following the recent turmoil in Syria, which is where our focus remains," he said.
"If the PM has any additional requests for NSW we are prepared to help."
