Doctors and child health workers from New Zealand have written to the Australian prime minister to condemn new secrecy laws in immigration detention centres and warn they will exacerbate the risks of abuse of child asylum seekers.

The latest letter from senior New Zealand paediatricians adds to a growing number of national and international professional bodies and individuals that have expressed concern about the conditions in Australian detention centres, and the increasing secrecy around them.

It follows the publication of an open letter last Wednesday from more than 40 staff who have worked in Australian detention centres, who challenged the government to prosecute them and said they would not be deterred from speaking out about abuses and poor conditions in detention centres.

The New Zealand open letter – addressed to Tony Abbott and opposition leader Bill Shorten – has been signed by senior medical professionals in New Zealand including Dr Ian Hassall, Dr Fiona Miles, Dr Alison Blaiklock, professor Brian Darlow, Dr Rosemary Parks, Dr Greg Williams and Dr Paul Trani.

“We are concerned for the children detained by the Australian commonwealth government in the immigration detention centres on Nauru and elsewhere,” the letter says.

“The circumstances in which there is no prospect of appeal or release are inevitably detrimental to many of the children’s development and mental health because of the impact on them of the depression, anger and desperation of their parents and other adults in their camps.”

“The secrecy provisions … which came into effect on 1 July will exacerbate these effects by severely limiting public oversight of conditions in the camp.”

The letter calls for a clear process for asylum seekers to resolve their claims and broader public oversight of the conditions in detention centres.

The new secrecy law that came into force on 1 July makes it an offence with a penalty of up to two years in jail for immigration staff and contractors who make unauthorised public disclosures. It has faced heavy resistance from many former staff in detention centres, who say they will continue to speak out about abuses.

The Australian Medical Association has also criticised the new laws, and the World Medical Association has taken the unusual step of issuing a statement criticising it.

Although the immigration minister, Peter Dutton, played down the impact of the laws on people who speak out about conditions in detention centres, emails obtained by Guardian Australia reveal that staff on Nauru were warned about speaking out about “anything that happens” in detention centres on Manus island and Nauru.