Several families trapped on Nauru have been granted entry into Australia for medical treatment, amid mounting pressure on the Morrison government to rescue all children off the island.

Three families of asylum seekers, comprising 15 people, left the Pacific nation on Monday, while Iranian, Somali and Lebanese families left on Tuesday, refugee advocates confirmed.

A Tamil father and daughter and another Lebanese family also departed the Nauru processing centre on Wednesday.

Prime Minister Scott Morrison has been urged by his own backbench to take immediate action to send asylum seekers to Australia, with doctors reporting that those in Nauru are mentally “shattered” after years in limbo.

Mr Morrison has spoken with Labor and crossbench senators about reviving a stalled 2016 bill to resettle asylum seekers in New Zealand, on a condition that they never enter Australia under any circumstance.

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,” Nauru said in a statement on Thursday.

“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.

“The doctor has a valid visa and a right to practice medicine on the island and we welcome the doctor back on the island as her services are needed,” Nauru’s statement said.

The Law Council of Australia has also called for asylum seeker children to be taken off Nauru.

“When you have the leading medical bodies in Australia saying unequivocally that the physical and mental health of children is deteriorating dangerously as a result of detention then urgent attention is required,” council president Morry Bailes said on Thursday.

-With AAP