Police have looked into reports that Ms Athanassiou, 39, had a history of family violence but it was not the focus of the investigation, Ms Howard said.
"While the post-mortem showed Sofia had some minor injuries, we don't believe these are connected to her death, which remains unexplained,'' Ms Howard said.
"We've also spoken with a large number of people, including those close to Sofia, but at this stage are not focussing on any links to family violence.
"It's disappointing that speculation about Sofia's past is being circulated, particularly while her family are grieving and her death remains unexplained.''
Ms Howard said police were still awaiting the results of laboratory tests, which could be six weeks away.
Anyone with information that could help police should call the Wellington station on 04 381 2000 or Crime Stoppers on 0800 555 111.