The children of refugees and asylum seekers on Nauru are likely to be transferred off the island by the end of the year, according to former attorney-general George Brandis.

Key points: The former attorney-general says the problem of children on Nauru has largely "gone away"

The former attorney-general says the problem of children on Nauru has largely "gone away" Scott Morrison has been facing political pressure to transfer the children

Scott Morrison has been facing political pressure to transfer the children The Australian newspaper is reporting that all the children will be off the island by the end of the year

Prime Minister Scott Morrison and Home Affairs Minister Peter Dutton have not disputed that timeline, instead saying they are working quietly without "showboating".

More children have been transferred for treatment, with Government sources confirming there are now 40 on the Pacific Island — down from 52 last week.

Political pressure has been mounting on the Coalition to transfer all children off the island, as senior doctors warn of increasing mental health problems.

Mr Brandis — who is now Australia's High Commissioner to the United Kingdom — says the end of year timeline is a reasonable expectation.

"In any event, this is a problem that's largely gone away," Mr Brandis said.

"There are hardly any children in Nauru and [Papua] New Guinea and we expect that by the end of this year there will be none."

The Morrison Government has lost its majority in the House of Representatives and crossbench MPs — and a handful of Coalition politicians — are agitating for change.

MSF has warned there are serious mental health issues affecting refugees living on the island. ( AP: Jason Oxenham )

Opinion polls show a majority of Australians want to see children relocated from the island and don't believe that would mean watering down tough immigration policies.

Mr Morrison — a former immigration minister — said his Government had been acting quickly to get children off the island.

"Children have been transferred off Nauru, that's been happening for some time," Mr Morrison told Sydney radio station 2GB.

"I haven't been showboating about it, I haven't been drawing attention to it.

"It's being done in accordance with out policies, our existing policies."

We want to clean up this mess: Dutton

Mr Dutton said he wanted to get the children of refugees off Nauru, but only in a way that does not encourage people smugglers.

"We closed the regional processing centre in Manus and … got the women and children off there," he said.

"We have done it there and we are int he process of doing it on Nauru, but we're doing it in a way that doesn't restart boats.

"We do want to clean up what is a significant mess..."

Former Human Rights Commission president Gillian Triggs welcomed news that more children were being transferred.

"Political events and community approaches have quite simply forced the Government's hand," she said.

"I don't mean to be lacking in grace about this, it's wonderful news and I'm sure the families and children and all of us are delighted for them, but the reality I suspect it is political."

'We need to be respectful of Nauru'

Mr Morrison said he was concerned that commentators were not showing enough respect to Nauru.

"I think people need to be very respectful of our neighbours in Nauru," Mr Morrison said.

"The denigration of Nauru and Nauruans is very un-Australian and I think it's very disrespectful, not just to Nauruans, but our Pacific neighbours more generally."

Sorry, this video has expired Angus Taylor says the number of asylum seekers on Nauru will continue to be reduced.

Last week Government MP Julia Banks called on the Liberals and Labor to stop political "games" and "pointscoring" and to focus on the children.

"It is wrong to say these children and their families are not detained," Ms Banks said.

"Sure they are not behind bars and they can walk about freely. But the will, especially the will of a parent with a sick child wanting help, it's a detention of their mind and their spirit."