The fighting erupted last week between the Kulumata and Kuboma people on the island, which is in Milne Bay province.
A team of police from the nation's capital, Port Moresby, were deployed on Tuesday to contain the situation, said Internal Security Minister Peter Tsiamalili. Tsiamalili said police commissioner David Manning was in charge of the operation, The Guardian newspaper reported.
"The team of police deployed today to the island have been instructed to contain and maintain order in the area, provide leadership on the ground and help start the peace process," he said.
The government is yet to release an official death toll, but government sources confirmed to The Guardian that 32 people were dead, while locals estimate that 15 people are missing.
An anonymous source, who did not wish to give their name due to fear of reprisals, said that the fight started last month when one man from Bwetalu village on the Kuboma side was killed during a fight over a football game.
He says Kuboma villagers allegedly retaliated by destroying the yam gardens of the Kulumata villages, which are very valuable and key to their livelihood. When the Kulumata villagers went to the authorities to make a complaint, they encountered a group of Kuboma villagers and fighting broke out.
Another local said it was "frightening to see such violence on their island", which is locally known as the "island of love".