A second body, that of a man, was found in Traunsee on Monday afternoon, about 5 km from the shore. He had bags containing stones and a concrete block tied to his hands. The concrete block concealed the woman's missing head.
Upper Austrian police chief Gottfried Mitterlehner told the press conference that detectives believe the man murdered the woman and then drowned himself.
The bodies have not yet been identified, and neither are believed to have been reported missing. So far, police have not found an abandoned car near the lake so it is not clear how the woman's body was transported to the water.
A coroner's report said that the woman was between 50 and 70 years old, was around 1.75 meters tall and weighed around 80 kilos. She was probably murdered between Christmas and New Year's Eve, and her body was then cut into pieces using a saw.
The first suitcase was found floating in the water by a man who was walking by the lake on the outskirts of Gmunden on Sunday. He pulled it ashore and called the police, who found parts of a female body inside it. On Monday morning a police dog discovered a second case, which also contained body parts.
One of the cases in which the remains were found. Photo: FOTOKERSCHI.AT