Two more passengers on the ill-fated Ruby Princess have died since Saturday evening - bringing the total number of passenger deaths to 18.
On Monday, NSW Health confirmed the deaths of the passengers - a 74-year-old woman who died at John Hunter Hospital and a 79-year old man who died at Northern Beaches Hospital.
More than 600 COVID-19 cases across Australia have now been linked to the ship which remains docked at Port Kembla.
Sixty-six crew members still on board have tested positive to the virus. In addition, 11 who have been evacuated from the ship with COVID-19 remain in Sydney health facilities.
Labor MP's Ryan Park and Paul Scully have joined unions to call for all on board to be tested. However on Monday, the state's deputy chief health officer Dr Christine Selvey ruled out testing the more than 1000 crew members.
"That's not a good strategy for a couple of reasons," she said. "First of all it won't change the way anyone's being managed on the ship, or the way the outbreak's being managed on the ship.
"Secondly testing everybody doesn't identify everybody who might be infected - that's because soon after infection the tests are negative during the incubation period - which is the time from when someone gets the virus to when they develop symptoms. So they will only test positive at the time of symptoms or just before it."
According to NSW Health all crew members who exhibit symptoms are tested, with 294 crew tested since the beginning of April - including 97 last Thursday. Some results are still pending.
Dr Selvey said some of the infected crew members were "already very close to recovery".
"Their infections have been spread out over a few weeks but they've just been tested recently which is why the numbers have gone up so high," she said.
NSW Health Minister Brad Hazzard said the ship was being managed by Aspen Medical, with oversight by NSW Police.
Detectives have conducted inquiries on board as part of an ongoing investigation into the docking and disembarking of the vessel in Sydney on March 19.
"Clearly there has been very close proximity in that ship and who was it that caused it, I think the jury's well and truly out, in the sense of who brought it onto the ship," Mr Hazzard said.
"... It's a very challenging issue for the medical people to track down the original source."
Mr Park, Labor's health spokesman, maintained that all crew needed testing.
"Surely for the welfare of the crew on board every single person should be tested, given especially that around half of all people tested so far have found to be positive," he said.
"When you have such a high number of people aboard testing positive it's imperative that the entire ship get tested to ascertain the extent of this public health crisis and to ensure those affected get the treatment they need and deserve."
Meantime in a statement Aspen Medical told the Mercury its multidisciplinary team had established and implemented "strict and robust infection control and isolation protocols" on board.
Aspen team members conducted daily health monitoring of crew isolated in their cabins - including temperature checks - and conducted COVID testing.
However, the statement said, Aspen Medical was "not responsible" for providing medical care.
"Carnival Medical Teams manage the medical care of their crew on the vessel and NSW Health will manage the medical care of any crew member deemed to unwell to remain on the vessel," the statement read.
"The Carnival Medical Team liaises directly with NSW Health. NSW Health determines the medical status of the unwell crew member.
"Aspen Medical is provided updates and is notified of any pending MEDIVACS from the vessel."