Vision of brawl on board the Carnival ship Legend.
It is still unclear if the family will face any charges for the fight, though Marine Area Command officials are now investigating it.
The Legend was on a 10-day trip throughout the South Pacific.
'He said, "Please Dad, please, call the Federal Police",' he added.
His 20-year-old son said "a lot of people are bleeding, a lot of people down".
Over the course of what some passengers had taken to calling the "cruise from hell", multiple violent incidents - including a fight in a nightclub and in an elevator - involving the extended family occurred, reportedly leaving some guests concerned for their safety and locking themselves in their rooms as a result.
Passengers cheered as the alleged troublemakers were taken off the ship.
A spokesman said: "Safety is the number one priority for Carnival Cruise Line, we take a zero tolerance approach to excessive behaviour that affects other guests and we have acted accordingly on Carnival Legend".
The Carnival Legend cruise ship is due to return to Melbourne’s Station Pier on Saturday morning
One passenger told Nine News: "We are so scared after witnessing a traumatic experience with yet again the same offenders".
Two passengers are dragged onto the floor before security officers appear to punch and kick the people grappling on the floor while a piercing scream can be heard in the background.
Zac, a member of the family that was removed from ship, reportedly told 3AW Radio that he believes he and his family were unfairly targeted, and claimed that the restaurant fight was instigated by another group.
Carnival Legend is an 88,500 gross ton ship and is based out of Melbourne, Australia including several calls in New Caledonia.
A NSW Police spokeswoman confirmed a planned police operation was under way on the ship.
They said threats had been made to stab and throw people overboard during what was described as a "cruise from hell".
"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".
One woman yelled that she had been mistreated on board as she was being removed.
"The ship's security team is applying our zero-tolerance policy in the interests of the safety and comfort of other guests", the company said.
From a SNAP recipient to Trump: Food box is a "terrible idea"
President Trump's budget proposes massive cuts to the program that provides more than 42 million Americans with food stamps. He says SNAP is efficient because it is a "free market model" that lets recipients shop at stores for their benefits.
AJ McCarron to become unrestricted free agent
The team put him on that list again on August 30, 2014, which meant he would miss at least the first six games of the season. McCarron, 27, entered the National Football League as a fifth-round pick out of Alabama with the Bengals in 2014.
President Mamnoon Hussain promulgates ordinance to include JuD, FIF among banned groups
The analysts fear that the FATF review this time could be tougher with some punitive action against Pakistan. He said that a similar operation would also be launched in Attock, Chakwal and Jhelum districts.