"For example if Jewish graves are desecrated we want Police to record that crime as more than just property damage," Ammunson said.
In releasing the letter, Moon cited the case of a European student club at the University of Auckland, which withdrew its application to affiliate with the University of Auckland after criticism and fears it was a thinly veiled white nationalist group.
The president of the fledgling club said it had become dangerous to continue in the face of "appalling rhetoric" and unfounded accusations of racism.
Moon said the closure of the European student club was something to be wary of.
"If what they say is indeed racist or promoting hate, then we should expose and ridicule it, not just shut it down," he said.
Moon said he planned to send a copy of the letter to all party leaders in Parliament.
Labour leader Andrew Little said there was a difficult line to draw between protecting free speech and pushing back against statements "calculated to cause harm or incite unhealthy responses".
Personally he was "a bit of a free speech nutter", Little said.
"We do have to, and sometimes on very difficult occasions, preserve the right of people to express views, even if sometimes they are unpopular or unpalatable to us. But there is a difference between that, I think, and clearly calculatingly harmful, prejudicial statements."
Prime Minister Bill English said there was generally a "pretty tolerant public discussion" in New Zealand.
"Occasionally there are some pretty strong views expressed and I think that's important that they are able to be expressed."
In Australia, the issue of hate speech has been more controversial. This month the Australian Senate rejected attempts to water down Australia's hate speech laws.
The Turnbull Government had proposed to change the law to replace the words "insult", "offend" and "humiliate" with the term "harass".
People who put their name to the letter organised by Moon were:
Assoc Professor Len Bell, Dr Don Brash, Dr David Cumin, Sir Toby Curtis, Dr Brian Edwards, Graeme Edwards, Dr Gavin Ellis, Sir Michael Friedlander, Alan Gibbs, Dame Jenny Gibbs, Bryan Gould, Wally Hirsh, Professor Manying Ip, Sir Bob Jones, Professor Pare Keiha, Assoc Professor Luamanuvao Winnie Laban, Dame Lesley Max, Gordon McLauchlan, Professor Paul Moon, Sir Douglas Myers, Assoc Professor Camille Nakhid, Sir Geoffrey Palmer, Professor Edwina Pio, David Rankin, Philip Temple, Dame Tariana Turia and Professor Albert Wendt.