On Monday private contractor Aspen Medical announced it was not responsible for providing medical care to the almost 1100 crew, despite health minister Brad Hazzard a day earlier telling reporters: "the crew who are on the ship are obviously being looked after through Aspen Medical. Aspen have been engaged by a number of governments around the world to look after cruise ships and crews".

International Transport Workers' Federation's Dean Summers said Aspen's announcement was "an incredible surprise".

"We've been told all along by the government that Aspen have been brought onto the ship to provide medical care to the crew and now we find that's not the case. We also find out from NSW Health that they're not responsible unless it's something critical.

"Where does that leave 1100 people? It leaves them completely bloody high and dry."

In a statement, Aspen Medical said it was responsible for setting up isolation protocols and providing training, education and advice, including to on-board medical crews as a "second opinion only".

It said Carnival Cruises' medical team would manage medical care of crew, and that NSW Health would care for anyone too sick to stay on board.

Mr Summers said the ship's medical team included just two doctors, three nurses and a paramedic.

He questions why crew remain on the ship, a so-called "flags of convenience" vessel which effectively has no home port so as to avoid paying taxes or meeting unfavourable regulations.

"It continues to regenerate infections," Mr Summers said. "[The virus] is slowly making its way through the whole ship, until someone becomes so critically ill they're medivac-ed."

"This ship is a black ship. We've got to get people off it. Treat them exactly the same as you would treat somebody coming off an airplane. Get them tested and put in hotel rooms away from the source of contamination."

The Ruby Princess left Sydney on March 8 and sailed to New Zealand.

A police investigation, likely to take another five months, is examining what Carnival Cruises knew about potential COVID-19 cases on board the ship before 2647 passengers were allowed to disembark in Sydney on March 19.

The Australian Border Force blames NSW health authorities for letting passengers disembark without adequate health checks.

The ship has since been linked to more than 660 Covid-19 cases and at least 20 passenger deaths

Another 139 crew have tested positive to the virus, up from 66 on Monday.

Mr Summers said a crew member was unaware of the ship's fatal associations when he was permitted to speak to the man last week.

"He was obviously set up by the company to call me and try to satisfy the company's obligation for the ITF to have communication with the crew. He was very focused on telling me how good the company was treating him, how happy he was. We had some small talk and I asked him if he was aware that there were a number of fatalities - I think at that stage there were 10 or 11 - and he was surprised that was the case."

A large proportion of the ship's crew hail from the Philippines, Indonesia, India and Sri Lanka.

On Tuesday, when asked about a parliamentary commission of inquiry into the Ruby Princess, Ms Berejiklian said it was important not to compromise the criminal and coronial inquiries already underway.

"Whilst the police investigation is focusing on potential criminal activity, it will be reporting on a whole range of issues so everything from go to woe is included," she said.

"I don't want anyone to feel the criminal investigation the police are conducting isn't robust."

She said her government would seek legal advice this week before considering the establishment of a commission of inquiry.

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"If the police are able to publicly provide to the community in five months' time about everything they've uncovered ... that is a positive for the community because any commission of inquiry would take at least six to 12 months," Ms Berejiklian said.

"We will not be leaving a single stone unturned."

NSW Police Commissioner Mick Fuller said he was willing to release all findings to the public if permitted, and that authorities had interviewed 200 witnesses over the weekend.

He said COVID-19 testing is still underway for crew members on the ship and daily conversations are taking place with NSW Health on moving the ship. Once NSW Health gives the all-clear on the health of crew members, Mr Fuller will ask the ABF to instruct the ship to return to its port of residence.

The commissioner on Monday said the disease was most likely spread on board by an ill food handler.

NSW Health Minister Brad Hazzard, meanwhile, on Monday said it was "unfortunate" 2700 passengers boarded the ship at a time when the coronavirus pandemic was already front and centre in the community's consciousness.

"It is a very unfortunate outcome but at the time that that ship sailed, which was March 8 from memory, there was COVID-19 well and truly," Mr Hazzard told reporters.

The Mercury has sought comment from the health minister's office.

- with AAP reporter Ashlea Witoslawski