Cellphone video from the ship shows passengers on the Carnival Legend tussling with each other and security officers amid shouting and screams from alarmed onlookers.
The video also shows security officers kicking passengers after they were down on the floor.
"We have a zero tolerance approach to excessive behavior that affects other guests," Carnival Cruise Line said in a statement. "In line with this policy, we cooperated fully with local authorities in Australia to remove a large family group who had been involved in disruptive acts aboard Carnival Legend.
"Our security team responded in several instances to extremely unruly behavior by these guests. One particular altercation in the nightclub began when the group physically attacked other guests."
However, the cruise line said, the "actions seen on the video by our security team are not in line with our Carnival values and policies."
Carnival and police did not say what started the fights, how many people were hurt and whether any charges were filed. Both the police and the cruise line are conducting investigations.
Another cellphone video, published by Melbourne radio station 3AW, showed passengers cheering as police removed the men from the cruise ship Friday.
NSW Police said in a statement they were told several men fought in the early morning hours Friday while the ship was about 220 kilometers (137 miles) off Jervis Bay, New South Wales. Security officers on the ship intervened and detained the men before notifying police, police said.
"About 1.30 p.m. (Friday), six men and three teenage boys were removed from the ship at Twofold Bay, Eden," the police statement said.
"A further 14 passengers, including women and children, also left the ship. The group were transported to Canberra where other travel arrangements were made."
As of Monday, no charges had been laid against the accused brawlers and no one had been detained, according to NSW Police. A spokeswoman said inquiries were still being made.
'They were looking for trouble'
The vessel was scheduled to sail from Melbourne to New Caledonia in the South Pacific and back over the course of 10 days.
Passenger Kellie Peterson told radio station 3AW she saw a lot of injuries.
"There's people been walking around with cut heads and hands and bandages everywhere," she told the station.
"They were looking for trouble from the minute they got on the ship," Peterson said, noting that she and her husband tried to move her three children out of the swimming pool when the group was around.
"Five of them surrounded my husband," she said. "And unfortunately my children witnessed it and they're scared. We've been told to watch our backs by this group. We're scared to go anywhere on the ship."
The remaining passengers disembarked Saturday in Melbourne. According to the cruise line's website, the ship is able to accommodate 2,100 passengers.
One passenger, Cindy Buglisi, told the Seven Network the situation was "horrifying, like people screaming, running around, throwing glasses, everything -- like nightmare."
Another, Jarrah Boliltho, said, "They (members of the family group) were roaming the decks just looking to pick on any Aussie they could find."
Some of the passengers told Seven Network they wanted full refunds from the cruise line. According to Cruise Mapper website, tickets for the cruise cost passengers at least $800 (AU$999).
Carnival said it would offer a 25% discount to these passengers on future cruises as a goodwill gesture.
"We sincerely regret that the unruly conduct and actions of the passengers removed from the ship may have prevented other guests from fully enjoying their cruise," the Carnival statement said.
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