The government has opened talks with crossbench senators about reviving a stalled 2016 bill to send asylum seekers to New Zealand, as long as they can never travel to Australia.
But at least one senator had a briefing on the bill postponed and they now expect it will not be addressed until the November sitting of parliament.
A multi-faith delegation of Christian, Muslim and Jewish leaders were meeting with Immigration Minister David Coleman on Thursday to call for all refugees in detention to be resettled.
"We need to bring them here and either offer resettlement in Australia or find another suitable country that welcomes them," Anglican Bishop Philip Huggins said.
Mr Coleman said Australia could only go down the NZ resettlement path if the laws to close future entry to Australia were passed.
"People smugglers don't deal with nuance," he said of watering down the laws to allow tourist and other non-permanent entry to the resettled asylum seekers.
The Law Council of Australia has also called for asylum seeker children to be taken off Nauru, after doctors from Medecins Sans Frontieres revealed their mental health had been "devastated".
The push came as one of the senior doctors Australia paid to be on Nauru left on Wednesday after she took a photo of an asylum seeker child.
International Health and Medical Services senior medical officer Nicole Montana arrived back in Australia but the Nauru government denied she had been deported.
"There was no removal order issued against the doctor nor was the doctor deported from the island as reported in media," the government said.
"It is regrettable that this occurred as the doctor has been an integral part of the medical services."
Under Nauru's local laws governing its regional processing centre, taking a photograph of the asylum seekers Australia put on the island is banned.
Dr Montana was welcome to return as her services were needed, the Nauru government said.
Australian Medical Association president Tony Bartone said there were many clinical reasons why a doctor would take a photograph of a patient.
"We've been calling for particular children with specific issues to be taken off the island as a matter of urgency," he told the ABC.