Gunmen from the rebel Liberation Tigers of Tamil Eelam (LTTE) ordered a family out of their home in Eravur and shot them dead, the military said, adding some of the victims were from a breakaway rebel faction.
Among those killed was a three-year-old boy, the military said.
The killings came as both the majority Sinhalese and the minority Tamil community marked their common New Year on Saturday.
President Mahinda Rajapakse in his New Year message appealed for unity in the ethnically-divided nation of 19.
5 million people.
"The observance of New Year traditions and rituals leads to the unity of the nation," he said.
"We should all come together to observe the New Year traditions, irrespective of all differences."
The Tigers on Friday vowed to hit back against an advance by government troops in the east of Sri Lanka where a breakaway faction known as the "Karuna Group" is collaborating with security forces to attack the Tigers.
The LTTE denied military claims that they