The ship is due to berth in Melbourne on Saturday.
Video of the scuffle, shared on social media, shows dozens of people fighting each other, security guards and other staff before the person filming the incident is confronted by staff.
It is still unclear if the family will face any charges for the fight, though Marine Area Command officials are now investigating it.
The 10-day cruise to the South Pacific was forced to make an unscheduled stop in Eden, New South Wales, on 16 February for 23 members of a Melbourne family to be removed following the brawl.
"He rang me about 1am this morning and said "Pease dad, please dad, call the federal police", Mr Barkho told the radio station on Friday.
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His son said "a lot of people are bleeding, a lot of people down".
Carnival Cruise Line bosses say disembarking an unruly family from a cruise was their "last resort". A further 14 passengers, including women and children, also left the ship.
Passengers described the trip as a "cruise from hell", according to AAP.
3AW said there were reports that up to 30 people were injured. An unnamed passenger filmed the ship's crew and security officers trying to break up the fight and, at one point, kicking two male passengers already on the ground.
She said she believed the violence had all been instigated by one large family group of at least 20 people who "came onto the boat wanting to fight people" and were using any excuse to start trouble.
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NSW Police confirmed in a statement that they had removed passengers from the ship and were investigating the incident: "Police are investigating an alleged fight onboard a cruise ship while it was about 220km off Jervis Bay".
"We take a zero tolerance approach to excessive behaviour that affects other guests and we have acted accordingly on Carnival Legend".
She added there had been a number of fights on board, including in a nightclub and in an elevator the next day, "and a big fight on the lido deck, which went on for about 45 minutes".
"Enjoy the rest of your cruise", one woman yells out.
"These incidents were complete isolated to this family group and out of character for the on board experience with Carnival Legend", Ms Vandekreeke said.
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The 10 other Delawareans who have died from the flu all had underlying conditions; Six of them had received a flu shot. As of February 3, the CDC's surveillance report noted that 48 states continued to experience widespread flu activity.
"The ship's highly trained security staff have taken strong action in relation to a small group of disruptive guests who have been involved in altercations on board".
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