In a departure from the message from her state Labor counterparts, Deputy Mayor Tania Brown, led the call. saying "I welcome the Ruby Princess to Wollongong".

"We need to show them some Illawarra kindness and [hope] that fair winds soon follow them home," she said.

The Ruby Princess docked at Port Kembla on Monday morning, as police announced a criminal investigation would be launched into how cruise ship passengers were allowed to disembark and return to their homes despite showing symptoms of COVID-19.

It has become the single largest source of COVID-19 cases in the state - with more than 620 cases, most acquired by passengers while on board the ship - and 11 deaths. Crew have remained on the ship, and hundreds are now showing symptoms.

The ship's arrival in Port Kembla created controversy, with Labor's health spokesman Ryan Park saying the NSW government was trying to "dump" its problems on the Illawarra.

But Cr Brown, a former chair of Destination Wollongong and a current member of Cruise Wollongong, said cruise ships had brought many financial benefits to the city.

"It's time for us to return the favour, and show compassion to the crew of the Ruby Princess which is now berthed in Port Kembla," she said.

"The Ruby Princess, like most cruise ships, is staffed by multinationals from over 50 countries. They spend up to nine months at a time at sea so they can send money home to their family. They need access to medical treatment and our care and compassion."

Liberal councillor Cameron Walters agreed, saying Cr Brown's comments were "spot on, perfect and precise".

"We can't just have this idea of turning ships away," he said. "Obviously we have medical professionals looking into this and... and I don't think it's time to be political about it."

Likewise, Greens councillor Mithra Cox called on residents to "be calm and be kind".

"I know there is a lot of angst in our community, but they are humans on that ship and they deserve medical care," she said.

"If that's in our hospitals here or in Sydney, I think we need to leave that to department of health."

Independent councillor Dom Figliomeni said it was "an international convention that ships in distress and seafarers in distress are taken care of".

"This is an unusual situation, it is one where it needs to be accepted there are people on board and they do need help and assistance in whatever way," he said. "However, we needed to make sure we do not disadvantage out community."

Late on Monday, NSW Health said any crew who required hospitalisation would be "allocated to a hospital primarily in the Sydney metropolitan area to minimise the impact on any one facility"

The ship could be docked Port Kembla for up to 10 days, for refuelling and restocking provisions required for its journey home.