Australia's coronavirus death toll stood at 34 on Sunday with 5,687 virus positive cases, officials said.

Health officials from New South Wales confirmed that there were 2,580 total infections now in the state and four people, including three passengers from Ruby Princess Cruise Ship, died on Saturday night.

During a virus update, NSW Health Minister Brad Hazzard said, "This is a very dangerous virus and it is still marching through our community. It has killed, at this stage in NSW, 16 people.''

The four men who died include a 91-year-old from Port Macquarie, an 80-year-old and a 76-year-old who were both being treated at Westmead Hospital and a 61-year-old being treated at Hornsby Hospital.

A total of 10 passengers of the Ruby Princess Ship that arrived last month at NSW have died due to COVID-19 and it has been linked to 600 infected cases.

The Ruby Princess Ship is still docked in the waters off Sydney and 250 crew members are awaiting test results.

NSW Police Commissioner Mick Fuller said a criminal or coronial investigation will be necessary to determine whether the operators of the Ruby Princess were transparent about ill passengers on board.

He said the 10 deaths linked to the cruise ship so far were a "significant" number for one incident.

From my perspective, there are many unanswered questions, and I certainly can't answer those for you today," Fuller said.

"There were thousands of witnesses out there who were passengers on the ship, who will have crucial information in relation to their health coming off of the ship, he said, noting records of the captain and doctors would also be investigated.

Fuller said he had received a letter from Carnival, which operates the Ruby Princess, ensuring him they would co-operate in anyway that is necessary.

Meanwhile, Queensland and Victoria each recorded smaller number of new cases while the chief medical officer Brendan murphy said more than 2,000 people have recovered.

However, he also reiterated social distancing instructions to keep community transmissions as low as possible.

"We're increasingly confident that if people continue to adhere to what we've been asking them to do we can prevent a situation like we've seen in many other countries of the world,'' he said.

"We're in a good place at the moment. We are achieving good control because the community has done what we have asked. They have done all of the things in the main that we've asked for them over the last weeks and it's been hard. It's been really hard,'' Murphy