The woman who was murdered in an act of cannibalism has been named as Cerys Marie Yemm.
Officers found Matthew Williams, 34, attacking the 22-year-old in the Sirhowy Arms Hotel, a halfway house for ex offenders in Argoed, a village near Ms Yemm’s hometown of Blackwood.
He was stunned with a Taser and arrested at the scene during the early hours of Thursday but later died.
Williams had only recently been released from prison.
The Independent Police Complaints Commission (IPCC) is probing his death and have also met the victim’s family.
Ch Insp Paul Staniforth from Gwent Police told a news conference on Friday that Ms Yemm’s family is being supported by officers.
He also said officers who attended the murder scene were being supported by the force’s occupational health department.
“The post mortem for Cerys will start today, although may not be complete for some time,” he added.
“Speculative comments about what happened and cause of death are unhelpful.”
Gwent Police said Williams was local to the area while Ms Yemm was from Blackwood, and the pair were known to each other.
The force said it is not looking for anyone else in connection with the incident.
Gareth Griffiths, who lives in Argoed, told BBC Radio 5 Live: “It’s not a massive village, everyone wants to know what’s happened. Everyone who doesn’t want the place to be there thinks it’s ammunition to use against the council to get it moved or shifted.
“We hear on the news that it has been cannibalism. Nobody wants to hear that, it must be a horrific way to die, it’s horrible, it’s unbearable.”
The property where the murder took place is used as temporary accommodation for homeless people.
IPCC Commissioner for Wales, Jan Williams, said: “I would like to express my sincere condolences to the families of the deceased at this sad and difficult time.
“Our investigators are gathering all relevant evidence to understand the full circumstances of what happened.”
BBC Wales reporter Stephen Fairclough in Argoed
People living in the small village of Argoed just north of the town of Blackwood have reacted to the disturbing events at the hotel with shock and disbelief.
The three-storey building where Williams is believed to have murdered the young woman sits in the middle of the village and the centre was a hive of police activity on Thursday as the investigation got under way.
One resident said the murder “is hard to believe in a small, quiet community village like this”.
Another described the police scenes as “chaotic” with emergency services vehicles “everywhere”.
One woman said: “It’s all very upsetting.”
Leon Gardiner, a councillor who has lived in the village for more than 80 years, said the killing has “hit the village for six”.
Argoed councillor Garry Lewis described the nature of the killing as “grotesque”.
Argoed Baptist Chapel secretary June Trace told BBC Wales that the Sirhowy Arms was converted into accommodation for vulnerable people several years ago.
She said it had a “fluctuating population” of people, often aged in their 30s or 40s, who would stay there for a time before moving on.
Despite concerns of some villagers when the plans were first put forward to convert the building, she said there had never been any trouble there.
However, other people living in Argoed said there had been issues at the hostel and police had been called to resolve problems there frequently.