The operator of the Ruby Princess cruise ship knew about coronavirus outbreaks while the vessel was at sea and "recklessly" put the lives of the passengers at risk, according to a lawsuit filed by the family of a man who died after disembarking.

Princess Cruises is being sued for nearly $1.6 million by the relatives of American national Chung Chen, who died earlier this month as a result of the pandemic when he returned home to Los Angeles.

The Ruby Princess is at the centre of one of Australia's biggest clusters after the ship visited New Zealand and Australian ports, and allowed passengers off in Sydney when many were feeling ill.

The virus tore through the ship and sparked cases in Australia and New Zealand. Sixteen cases in Hawke's Bay have been linked back to the ship which docked in Napier on 14 March.

Detectives have begun interviewing thousands of witnesses about what they knew about potential Covid-19 cases on board the cruise ship before it returned to, and docked in, Sydney more than three weeks ago.

Since disembarking in Sydney, 18 passengers from the ship have died and hundreds of confirmed cases have been linked to the vessel.

Chung Chen's widow, Juishan Hsu, and daughter, Vivian, are seeking damages in the District Court of California as the death toll from cases linked to the infamous ship reaches 21.

Princess Cruises "chose to place profits over the safety of its passengers, crew and the general public in continuing to operate business as usual", the lawsuit claims.

The wife and daughter of the deceased man, who were both also infected by the virus, didn't know there was an outbreak on the ship until after they got home.

"The case against Princess Cruises is based on corporate negligence and corporate gross negligence, they sailed on March 8 knowing that there was a huge risk of putting their passengers exposed to COVID-19," the family's lawyer Debi Chalik told the ABC.

"While they were on the ship, they had no idea anything was going on.

"There was no reason for them to know that anything other than an ordinary cruise was happening. They didn't realise there was an outbreak on the ship until after they got home."

The lawsuit, filed on Wednesday, accuses the company of allowing passengers to board without being screened to join crew who had already been exposed to the deadly virus.

This negligent action allowed the pandemic to "run rampant" on board the ship, the claim says according to The Sydney Morning Herald.

"They didn't even bother to notify the passengers that there was an actual outbreak, allowing the sailing to continue as if it were a normal cruise, up until the time it returned to Australia three days early," it claims.

A criminal investigation into the ship and its links to the coronavirus cases continues as the parent company Carnival Corporation denies the allegations.

"As this is the subject of active litigation in another country, we do not wish to add further comment at this time," a spokesman said according to the SMH.

• Covid19.govt.nz: The Government's official Covid-19 advisory website