Allegations include women, men and minors being sexually assaulted, raped and violently attacked.
There are claims on social media of druggings - of people being chased at night - of people being attacked in their sleep or when passed out.
Detective Senior Sergeant John Van Den Heuvel said people with allegations should contact police or survivor support services rather than posting about it online.
"Come forward, tell us your story. We will treat you with utmost respect and sensitivity.
"We will investigate thoroughly and hold anyone to account."
A dozen police investigators are working the case, with more to be added if there are additional complaints.
Police will not say how many complaints they have received or how many people they are investigating.
They describe the allegations as historical - although some survivors allege attacks happened just weeks ago.
A Wellington man - who is also musician - said that late one night earlier this year he chanced upon what he now believes to be two of the alleged attackers in central Wellington.
He said they were aggressive, yelling at passers-by as they strong-armed an upset and intoxicated young woman down the street.
He asked the woman if she was all right and she said she needed help.
"One of the guys turned to me and was like, 'eff off b*tch, you don't know who I am... We'll smash you if you do anything'."
He said he followed them further down the road and when the men got distracted he bundled her into a taxi.
They started pushing him and again threatened to attack him but some of their friends showed up and hustled them away, he said.
The man said he thought they were planning on taking her elsewhere and assaulting her.
"It really did seem that they were trying to take her somewhere against her will, with my fear being that she'd maybe been drugged.
"The way that they are carrying her and handling her - that's what really made me ... fearful for her safety.
"The reason I intervened was the fear of a sexual assault taking place."
He said when he saw the posts on social media naming the alleged attackers he looked them up and realised it was the same men from the incident.
Rape survivor and victim advocate Louise Nicholas, speaking for a group of the complainants, said they wanted others assaulted by the group to step forward.
"Come and talk to police and just know that you are extremely safe to do so."
Wellington City Councillor Tamatha Paul said she personally knew some of the complainants.
She convened a meeting yesterday between some of the survivors, police, Nicholas, and representatives from Wellington Rape Crisis and other survivor advocacy groups.
She was not surprised to hear of assaults like this happening in the capital.
"There is some information coming out in the next few days that shows that the number of assaults and sexual assaults in Wellington is amongst the highest in the country.
Paul said she believed the problem was widespread.
"One of the main messages that I've seen over the last few days is that actually this is really prevalent in the music industry but also in New Zealand generally."
The police have urged people to refrain from naming the men or posting personal details, as it could impact the police investigation.
Anyone with information should contact Wellington Police on 105, and reference Operation Emerald.
Where to get help:
• If it's an emergency and you feel that you or someone else is at risk, call 111. • If you've ever experienced sexual assault or abuse and need to talk to someone call the confidential crisis helpline Safe to Talk on: 0800 044 334 or text 4334. (available 24/7) • Male Survivors Aotearoa offers a range of confidential support at centres across New Zealand - find your closest one here. • Mosaic - Tiaki Tangata: 0800 94 22 94 (available 11am - 8pm) • If you have been abused, remember it's not your fault. • Wellington HELP has a 24/7 helpline for people who need to speak to someone immediately. You can call 04 801 6655 and push 0 at the menu.