A coalition of some of Australia’s biggest humanitarian and human rights organisations have given the federal government a deadline to get all asylum seeker and refugee children off Nauru, as the health and safety crisis on the island worsens.

World Vision, alongside more than 30 other organisations and advocacy groups, has called for parliament to bring the more than 120 children and their families to Australia or settled in a safe third country by Universal Children’s Day on 20 November.

It follows a unanimous motion passed by the Australian Medical Association’s federal council on Saturday, calling for the government to “act urgently to guarantee the health and wellbeing” of the children and their families.

The coalition includes World Vision New Zealand, the Australian Council for International Development, the Refugee Council of Australia, St Paul’s Anglican Cathedral, the Anglican Diocese of Sydney, Australian Lawyers Alliance, and the Australian arms of Save the Children, Oxfam, Amnesty International and Plan International.

“We are calling for common sense, for courage, for compassion and for leadership from our political leaders to resolve this situation,” World Vision Australia’s chief executive Claire Rogers said in Canberra on Monday.

“This harmful, secretive, and dysfunctional system of detention must end.”

Melanie, age three, likes to play with Lego, and she enjoys cooking and painting. Her family have been on Nauru for five years. Her mum says Melanie pretends to be a doctor when she plays. Photograph: World Vision

“We abhor any form of unfair vulnerability created by a situation and this is actually of the Australian parliament’s making,” Rogers told Guardian Australia.

“There’s a quite clear contravention of the refugee convention, and also we believe very strongly a breach of the rights of the child.”

The campaign highlights a number of children, including three-year-old Melanie*.

“It is so difficult to live in Nauru,” her mother said. “I wish on nobody that they are stuck here like us.”

There is growing alarm at the mental health and wellbeing of children on Nauru. The Australian immigration minister, Peter Dutton, has repeatedly denied them access to healthcare in Australia, despite medical advice that it is a matter of life and death. Dutton has repeatedly been taken to court over these decisions, and lost, with at least 12 children so far brought to Australia for care under court order.

Some have attempted suicide multiple times.

Guardian Australia reported earlier this month on the case of a girl suffering a severe major depressive disorder and resignation syndrome, a medical condition observed mainly among refugee children in Sweden but now found in several children on Nauru. Children suffering the condition – a reaction to extreme trauma – withdraw from interaction, refusing food and water and communication. It is potentially fatal.

Rogers said there was no “easy answer” but the coalition wanted the situation resolved to ensure they “have an opportunity to grow up with hope”.

George, two, likes to play with his toy car and to write. He was born in Nauru – the family have been on the island for five years. His mother says: ‘He doesn’t talk yet, but he loves to write. I think he is going to be a writer, like his father.’ Photograph: World Vision

“These children are caught between a desire to stop deaths at sea, which we absolutely don’t want to see an increase in, but there’s no justification for locking children up to create that outcome, that’s not the solution,” said Rogers.

Chief executive of Oxfam Australia, Helen Szoke, said Australia had a strong economy and a proven history of managing resettlement effectively, and needed to increase the number of refugees it assisted.

“As humanitarian organisations we are seeing first hand that across the world an unprecedented number of people have been forced to flee their homes,” she said.

“At the end of 2017, 68.5 million people were displaced, by wars and crises, like those in Syria, Yemen and countries I’ve visited like South Sudan.”

There are also around 40 children born in detention during the past five years who have never known another life.

Many have witnessed or been subjected to abuse or harm, including but not limited to the hundreds of incidents documented in the Nauru Files, published by Guardian Australia in 2016.

Rogers has been at the helm of World Vision Australia for around 18 months, and said one of the challenges was realising she would be advocating for children in her own country, not just those in the developing world.

“As the largest humanitarian organisation in the world focused on child wellbeing and in particular, vulnerable children, we felt it was most appropriate for us to recognise we have vulnerable people on our own shores,” Rogers said.

Dutton has maintained the children on Nauru are not in detention because those who have not moved from the centre into community accommodation are free to come and go, and that the Coalition government has technically closed both offshore detention centres, as well as 17 onshore.

“We know from many psychological studies over many years, at least 100 years, that human response to stress and lack of autonomy is quite profound psychologically,” Rogers said in response.

“This is not a normal environment for children, particularly these children. While the Nauruans also live on the island, they’re free to come and go as they wish, and they’re living with their families and their extended families, which is a very different situation to these children.”

The Australian Medical Association president, Dr Tony Bartone, said the children and families held indefinitely on Nauru must be given urgent access to appropriate healthcare, transparently. Bartone said while International Health and Medical Services staff were “doing their best in trying conditions”, the Australian public needed to be informed.

“The AMA repeats its call for a delegation of independent Australian health professions to be allowed to visit and examine the asylum seekers – adults and children – and report their condition to the Australian parliament and the Australian people,” said Bartone.

“It is our responsibility to care for these people. It is all about human rights. It is the right thing to do.”

On Monday morning, Labor’s spokesman for immigration, Shayne Neumann, said the Australian government should take up New Zealand’s offer of resettling some refugees, given it had managed to do it with the US.