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Police believe they know who killed New Zealand nurse Michelle Beets in Sydney but the suspect can't be found.

Sydney's Sun-Herald reported yesterday that, for legal reasons, homicide detectives had refused to make an appeal or name the man until they had exhausted all other avenues.

Earlier, it was reported that a male nurse was sacked from Royal North Shore Hospital after Ms Beets reported him for stealing pharmaceuticals from the hospital.

The staff member has not been named, but police have been interviewing former colleagues of Ms Beets at the hospital.

On Saturday, the de facto husband of Ms Beets spoke publicly for the first time since the death of his "wonderful partner and friend".

David Grant said her death had been a tremendous shock but he wanted to thank those who had helped the family and who attended her funeral on Friday.

Almost 1000 family and friends packed into Our Lady of Dolours Church in Chatswood to remember and pay tribute to the 57-year-old nurse who was found stabbed to death on the veranda of her Chatswood home on April 27.

"In this extremely sad time, I would like to express my gratitude to all those who have helped in the aftermath of Michelle's tragic death," Mr Grant said in a statement issued by a family friend.

"Family, friends, the staff at Royal North Shore Hospital, the police and other emergency and funeral services all have shown outstanding support.

"Michelle was a wonderful partner and friend and her sudden death has been a tremendous shock.

"The funeral was a chance to say goodbye and I'm grateful to all those who organised and attended it."

His statement was prompted in part by a large number of media requests to speak to Mr Grant, which he has declined, the family friend said.

"This is a time of grieving and I would now ask the media to respect the privacy of myself and Michelle's family and friends," he said. "Michelle will always stay in my heart."

Police are seeking public help to identify a man wearing a green top and carrying a backpack seen fleeing the murder scene.

Police inquiries last week stretched to the search of three Sydney rubbish tips, with detectives hoping to find evidence linked to the murder.

After several hours of searching, police, who said they were conducting the searches based on new information, said they had found nothing linked to the murder.

- Staff reporter, AAP