Serial killer Peter Tobin refused to admit to any more murders as detectives questioned him on his deathbed.
Tobin, 76, died on Saturday in the Royal Infirmary of Edinburgh after becoming unwell at HMP Edinburgh where he was serving life sentences for three murders, police said.
But detectives have long suspected that Tobin had more victims and hoped he would give up his secrets before he died.
He was serving a life sentence for raping and murdering Polish student Angelika Kluk, 23, and hiding her body under the floor of a Glasgow church in 2006.
The killer was also serving life terms for the murders of 15-year-old schoolgirl Vicky Hamilton, of Redding, near Falkirk, in 1991, and 18-year-old Dinah McNicol the same year. Their bodies were found 17 years later, buried in the garden of his former home in Margate, Kent.
Police believe he is responsible for the murders of other women because he had at least 40 aliases and 150 cars during his life.
It is understood that detectives spoke to Tobin in his final days in hospital in a bid to get him to admit to any other crimes.
Detective Chief Superintendent Laura Thomson, head of major crime at Police Scotland, said: "Recent attempts to encourage him to do the right thing and share any knowledge he may have which could assist the police were unsuccessful.
"While we have no current lines of investigation into Peter Tobin, we welcome any information in relation to his activities."
The Sunday Mail previously reported that Tobin had cancer and had fallen and broken his hip. The publication said the killer was refusing food and medication.
Last month a photo was circulated of Tobin "chained to a hospital bed" in a hospital gown, appearing seriously ill.
The family of Vicky Hamilton said they no longer wish to talk about Tobin.
The statement from siblings Sharon, Lee and Lindsay on Facebook read: "We remember Vicky, we remember her laughter, her smile and we want to keep that memory after all the years of having no idea what had happened to her, followed by heartbreak of losing our mum not long after Vicky went missing.
"He does not deserve any more of our family's thoughts.
"If he has taken more victims, our hearts go out to their families and can only wish one day they get the closure they so badly deserve.
"We will not be celebrating any passing but instead will be remembering Vicky, Angelika and Dinah along with any other victims, and we respectfully ask for others to do the same."
Former Strathclyde Police detective David Swindle, who led the investigation into Tobin, said he had no doubts the serial killer murdered more people.
"Peter Tobin is evil. He's pure evil," he told the BBC.
"This is someone who had no respect for humanity. This is a coward, who has taken his secrets to the grave."
Police Scotland said: "Around 6.04am on Saturday, October 8, 2022, officers attended at the Royal Infirmary of Edinburgh following the death of a 76-year-old man.
"The death is not being treated as suspicious and a report will be submitted to the Procurator Fiscal."
The Scottish Prison Service declined to comment.
