Norwegian Cruise Line is letting guests disembark the ship if they like with the cruise line providing a flight credit of up to $350 per person to Aukland.
On Friday, a man phoning from the ship told The Age passengers were devastated and crying.
Thousands of cruise ship passengers are being forced to make alternative travel plans after the Norwegian Star broke down off the Victorian Coast.
Distressed passengers were filmed erupting in anger on the disabled ship, chanting "we want answers".
Norwegian Star has suffered an azipod propulsion failure and as a result, being towed back to port.
All guests can stay onboard while the ship is docked and enjoy additional time in Melbourne and then continue onto Auckland on the revised itinerary once the repairs are complete.
Nonetheless, the cruise line's spokeswoman said the ship's upcoming itinerary from Auckland, beginning February 18, is expected to continue on schedule.
All guests onboard were provided a full refund, as well as a 50 percent future cruise credit.
"We're stuck in the middle of the ocean".
A woman, who also didn't wish to be named, said her friend was on board the ship and had phoned to tell her about the situation.
A spokeswoman for the company, Anne Wild, described the latest fault as "very usual" and said passengers would be financially compensated.
The Australian Maritime Safety Authority said a representative from Melbourne's port would board the ship when it reached the Port Phillip Bay heads, which was expected to happen early this afternoon.
Another wrote on Facebook: 'We have no engines for propulsion!