South Australia has recorded a small jump in confirmed cases of coronavirus, bringing the state’s total to 409.

Two more cases have been diagnosed in SA overnight, an improvement on Saturday’s 11 new cases.

The national death toll from the virus rose to 34 on Sunday after four men died in NSW.

Three of the new deaths were passengers on the Ruby Princess cruise ship.

A criminal investigation will be launched into how the cruise line operator Carnival Australia was allowed to disembark the Ruby Princess in Sydney.

More on 7NEWS.com.au

There have not been any deaths reported from coronavirus in South Australia so far.

In the video below: What now for cruise ships off Australia?