Norwegian Star passengers have been delayed and some have abandoned their dream cruise to New Zealand after the propulsion system stopped functioning on Friday off Wilsons Promontory on a multi-stop cruise to New Zealand.

The crippled vessel was dragged by tug boats to Port Melbourne's Station Pier early on Sunday morning.

A spokeswoman for operator Norwegian Cruise Line defended the ship.

"There is no safety issue in relation to this ship; the issue is speed," she said.

The spokeswoman said the ship had not lost power, and all services were still operating on board; the problem lay solely with the propulsion system.

The system earlier struck trouble on a journey between Hong Kong and Indonesia on January 16.

It was unusual to have two propulsion system failures and it was not yet clear whether the incidents were related, the spokeswoman said.

The delays meant the ship would miss some scheduled stops, including Milford Sound in New Zealand.

The spokeswoman said passengers were aware of the shortened trip. She said they had been getting hourly updates from the captain and that the operator expected to arrive in Auckland on time, on February 18, but more stops might still be cancelled.

Engineering crews were inspecting the fault.

"In terms of fixing it, I understand it is not a complicated fix. It is a matter of parts. It is not like you can go down to Bunnings and get these parts," she said

About 10 per cent of the 2000 passengers on board had decided to leave the ship.

All passengers have been offered a full refund, plus 50 per cent off their next Norwegian Cruise Line cruise, regardless of whether they stay aboard or leave.

Passengers who abandon the cruise will also receive $350 per person for flights to New Zealand and $300 per ticket to compensate for flight rescheduling penalties.

Passengers disembarking were preparing to either abandon the cruise or wait up to five days for the repairs.

US couple Trevor and Ashley Wagner were cutting their losses and booked a flight back home on Sunday morning.

"It wasn't as desperate as some people were saying but it was very disappointing," Ms Wagner said.

"We figured we would save the vacation time and take the trip again another time."

Mr Wagner said the Norwegian Star operator's offer of flights to New Zealand was not the dream trip they had planned.

They will rebook the trip another time, he said.

"We were two days at sea and were supposed to see New Zealand," Mr Wagner said. "We are cutting and running."

Edward Benton, of Dallas, Texas, said the staff were helpful and friendly during the trip, in which the cruise liner was adrift for two days in the Tasman Sea.

Edward Benton hopes to continue on the Norwegian Star.  Photo: Deborah Gough

He said he and his travelling group would go to the Queen Victoria Market and Melbourne Zoo on Sunday and wait to see if the ship could be fixed.

"Who knows after that?" he said.

"If the ship moves, I am going with the ship. If not, I am going to fly to New Zealand."

Mr Benton said he had not seen any evidence of the passengers chanting for "answers" as reported earlier.

Mike Clark, of Fort Worth, Texas, part of the same group of travellers as Mr Benton, said while he could fly to New Zealand he had already missed out on a trip to Milford Sound.

The ship was 70 nautical miles out at sea when trouble with the propellers stopped it from moving, Mr Clark said. But he felt lucky that it was not heavily buffeted by waves.

Wayne Mills and his partner, Kerry Gunnell, of Rosebud, were continuing on with the cruise, which they boarded in Melbourne. Ms Gunnell said she would remain on the ship as long as it took.

"We are having a ball," she said. "I am not going home to cook and clean." 

Ron Sullivan, of Christchurch. Photo: Deborah Gough

Retiree Ron Sullivan, of Christchurch in New Zealand, was quietly happy to spend more time in Melbourne.

"I live in New Zealand and I am quite happy to stay four or five days in Melbourne," he said. "I want to go to the races if I can.

"The service was fantastic on the ship."

Mr Sullivan said he had been on six or seven cruises and would again.