"We must act now," they wrote. "The rapid spread of MPX indicates a failure of the public health strategies that were implemented early on overseas."
They want a dedicated monkeypox response team; a vaccine plan prioritised; better, stigma-free, public health communication; and support for self-isolation.
Rich told RNZ the organisation had been constructively working with the Government on a response but was concerned how similar current plans were to those of Northern Hemisphere countries.
"What we're seeing at the moment is that in the Northern Hemisphere, the approaches that they've been using to try and control monkeypox have not been working and the [case] numbers are increasing."
Since early May, more than 18,000 cases have been confirmed or suspected in more than 70 countries outside of where the virus was usually endemic.
In New Zealand, three cases have been confirmed - two of whom have recovered. The Ministry of Health considers the public health risk to be low-to-moderate, but with a high risk of more cases being imported.
Rich said a post-exposure vaccine approach, known as ring vaccination, was "not going to be enough" and that it should instead be pre-emptive and used as a primary tool instead of relying on contact tracing and testing.
"This is not a criticism," he said. "This is just saying that we have the advantage ... of being able to learn about what is or isn't working in other countries."
University of Auckland associate professor Peter Saxton said procuring pre-exposure vaccines was needed so New Zealand could "stay ahead of the virus, rather than chasing an infection that we see moving fast among most at-risk communities overseas".
He was concerned that infections would soon start being missed and the virus would "start spreading locally".
"We still have a short window of opportunity to act before monkeypox becomes established."
The Ministry of Health said it was "working with Pharmac to secure access to third generation smallpox vaccines that can be considered for the targeted prevention of monkeypox".
RNZ understands health officials and manufacturers are discussing a possible delivery schedule for a vaccine, as well as antiretroviral treatments.
'I'm quite worried to be honest with you'
Gay, bisexual and other men who have sex with men (MSM) have been disproportionately affected in the current global outbreak but anyone can be infected with monkeypox.
The Ministry of Health said the risk of transmission was "considerably lower" than Covid-19 or measles, "given it requires very close contact".
It could be transmitted person-to-person by close contact with skin lesions, body fluids, respiratory droplets and contaminated materials such as bedding, but was not likely to be a sexually transmitted infection.
Dr Massimo Giola, is a member of the New Zealand Sexual Health Society executive, said the country needed to act "before we have a major problem in our hands".
Giola is gay and studied infectious disease in Italy, during the 1990s, "right at the top of the Aids pandemic". The current monkeypox outbreak made him feel like he was reliving that time but in "fast forward" and he wanted to see a stronger outbreak response.
He said he understood why some MSM "feel under threat".
"I'm quite worried to be honest with you."
There were challenges in creating a response without stigma, Giola said.
Specifically, officials needed to carefully juggle acknowledging the disproportionate rate at which the MSM community was being affected without stoking the homophobia that the outbreak had stirred up online, including people calling monkeypox a "gay disease" or thinking it only affected the MSM community, he said.
The struggle of this was already coming through in patients he saw. Giola had started talking to patients inquiring about HIV-prevention drug PrEP whether they knew of monkeypox and where to find information.
"Always, always, always the question I get is: 'when are we getting the vaccine?' So people are very aware there is a vaccine and they definitely want to have access to that."
'Leadership, bold action' needed
The Burnett Foundation's Rich said they were not trying to create panic but officials needed to be "very careful" to get the response right.
"We know from our experience with Covid we have unique opportunities in New Zealand to learn from the rest of the world."
Similarities to the Covid-19 pandemic response were mentioned in the letter to Ardern.
"As with Covid-19, an effective response to MPX requires leadership, bold action, and comprehensive resourcing at a level commensurate with the threat of this novel global public health emergency."
RNZ asked the Ministry of Health a series of specific questions about the concerns raised in the letter.
They went unanswered, but the acting public health director, Harriette Carr, said the ministry "acknowledges the concerns raised in this letter".
Carr also said public health advice had been worked on since "the early stages of the current global outbreak" for the general public and health professionals.
RNZ has also approached the offices of the Prime Minister, Minister of Health, and Associate Health Minister for comment.