The spokesperson said: "Threatening comments towards [homeless] people are also unnecessary and should cease".
Last week, one of the men involved apologised on social media for his actions.
He blamed his actions on drunkenness before hitting out at those who called him privileged.
"Just want to out it out there that I know what I did was completely f***ed up and I regret it so much.
"I was extremely drunk please don't think I am proud of myself I am truly paying for what I did and acknowledge what I did and hate myself for it.
"[I] wish I could take it back but I simply can't. I'm actually not the privileged c*** of a person I am being made out to be. Yes I made a stupid heartless mistake when I was drunk."
The man, who admitted to being one of the two people who threw rubbish and food at the homeless man, also claimed he's previously helped homeless people by volunteering at a soup kitchen.
Anyone with information they think might assist Police, should contact 105 quoting the file number 220122/2740.
The homeless community of Auckland's CBD is among the most visible parts of Aotearoa's housing shortage.
The everyday struggles faced by those on the streets lead to dramatically reduced life spans.
Homeless New Zealanders are dying 30 years younger than those with a roof over their heads, a 2020 study found.
"Homeless people are dying because healthcare is so out of reach," Debbie Munroe, a volunteer at Waka of Caring earlier told the Herald.
The NZMJ study found that the average age for a homeless New Zealander to die was 45 years. Of the 70 suicides, it was younger at 38 years.
Researchers of the study examined coroners' reports of 171 deaths of New Zealanders with "no fixed abode" when they died during 2008 to 2019.
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