A chief constable has slammed "sensational and unsubstantiated claims and speculation" made following the conviction of a taxi driver for his second murder.
Christopher Halliwell, 52, formerly of Swindon, Wiltshire, murdered Becky Godden, 20, in January 2003 and Sian O'Callaghan, 22, in March 2011.
He was handed a rare whole life order - meaning he will never be released - at Bristol Crown Court last month after being convicted of Miss Godden's murder.
Wiltshire Police are now working with other forces and the National Crime Agency (NCA) to identify possible further victims of Halliwell.
Following his trial, reports linked Halliwell to other murders including missing chef Claudia Lawrence, who failed to turn up for a shift at work at the University of York in 2009.
In a column issued through the force, Wiltshire Police Chief Constable Mike Veale said the force had not uncovered any links between Halliwell and other murders "at this time".
"As a result of the obvious emotions and complexities of this case, the public criticism and unjustified challenge of Wiltshire Police was entirely predicted and expected, but the force made the ethical decision to maintain its position of not rising to the sensational and unsubstantiated claims and speculation," he wrote.
"We did this because we believed these sorts of claims would create a media frenzy and in turn lead to the families of people who have gone missing or tragically been murdered being re-traumatised and put into impossible positions.
"Their expectations, their feelings and their distress would be unnecessarily dragged once again into the media spotlight - this is something which I believe is unforgivable, injudicious and insensitive.
"This was reinforced to me when I spoke to the mothers of some of those named during the coverage of this case, who told me they had been traumatised and distressed by this unfounded speculation involving their loved ones."
Mr Veale paid tribute to the investigation team, led by Detective Superintendent Sean Memory, who brought Halliwell to justice for Miss Godden's murder.
He said the team should be congratulated and commended for their meticulous work as they had "undoubtedly brought this investigation from the edge of a precipice to a safe conclusion".
The charge of murdering Miss Godden was withdrawn in May 2012, after a High Court judge ruled confessions made by Halliwell could not be presented to a jury.
Halliwell was arrested and taken to meet then Detective Superintendent Steve Fulcher following his arrest for kidnapping Miss O'Callaghan.
Mr Fulcher repeatedly refused Halliwell's requests to be taken to a police station and have a solicitor, and did not caution him.
Halliwell eventually confessed to Miss Callaghan's murder and led officers to her body in Uffington, Oxfordshire.
He then confessed to killing Miss Godden in 2003 and took police to her remains in Eastleach, Gloucestershire.
A High Court judge ruled the confessions could not be used as Mr Fulcher had breached rules governing the questioning of suspects.
Mr Fulcher was found guilty of gross misconduct by a police disciplinary panel and handed two final written warnings. He resigned months later.
Halliwell was charged with murdering Miss Godden in March 2016 following a new investigation by Wiltshire Police.
In interviews following Halliwell's conviction, Mr Fulcher - now a consultant in Somalia - criticised the force's handling of the case.
Mr Veale wrote: " There has been much speculation in the press in relation to other women who may or may not have been a victim of Halliwell.
"This speculation is not helpful and is very distressing to the families involved. At this time Wiltshire Police has not uncovered any links between Halliwell and any other murders across the country.
"There is also an assertion by commentators that Wiltshire Police did not liaise with other forces across the country to identify any potential links to Halliwell. This is also not the case."
Police teams have obtained 1,736 statements, completed 3,546 actions, seized more than 2,717 documents and catalogued 2,556 exhibits, he added.
Following Halliwell's arrest, forces were notified of the circumstances of both murders and the facts known at the time. These were shared with an NCA database.
Mr Fulcher has called for changes to the Police and Criminal Evidence Act to empower senior officers in such cases.
But Mr Veale said: " I believe that if the current legislation is ethically followed and delivered in line with the codes of practice, common sense can prevail and the right outcomes can be achieved without evidence being inadmissible."
He added that anyone with information linking Halliwell to other murders should contact the force.
North Yorkshire Police dismissed claims by Mr Fulcher that there were links between Halliwell and Miss Lawrence.
Following Halliwell's conviction, the former detective said the murderer's father lived a few streets away from where Miss Lawrence went missing in 2009.
But on Monday, a North Yorkshire Police spokesman said this was incorrect and that there were no known links.
The spokesman said: "North Yorkshire Police's Major Crime Unit has shared information with the investigation team from Wiltshire Police which established that Halliwell's father was not a resident of York or the North Yorkshire area. He also passed away in 1992.
"It can be confirmed that on the information provided by Wiltshire Police, there are no known links between Halliwell and the Claudia Lawrence case.
"The senior investigating officer in the Claudia Lawrence investigation has been in contact with both Joan and Peter Lawrence following last weekend's speculation of these links, particularly that Halliwell's dad lived around the corner. This type of speculation does not help the family."