"We don't know the identity of the victims," a local police official said by telephone.
"We are now digging the area because there could be more bodies.
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The defence ministry said in a statement that the bodies were "badly putrefied and in an unidentifiable condition."
The mutilated bodies were found in a rubbish dump at Wennapuwa, just north of the Bandaranaike International airport and 60 kilometres (37 miles) north of the capital Colombo.
In the same region in March, police discovered the bodies of five ethnic Tamils who were killed execution style with their hands hands tied behind their backs and blindfolded.
Two Tamil aid workers attached to the local Red Cross were found shot dead in the central district of Ratnapura on Saturday, hours after they were abducted by gunmen posing as policeman in the capital of Colombo.
The latest discovery was made a day after police ordered hundreds of ethnic minority Tamils out of the capital at gun point.
The Supreme Court on F