Police are warning women in Bristol not to walk home alone after dark because landscape architect Joanna Yeates's killer remains at large.
They acknowledged the alarm in the local community sparked by the grim discovery of the 25-year-old's snow-covered body on Christmas Day.
But they reassured the public that patrols had been stepped up in the upmarket Clifton area of Bristol where she lived, and that they were "determined to find out" who killed her.
The comments yesterday came the day after officers from Avon and Somerset Police freed Miss Yeates's landlord Chris Jefferies on police bail pending further inquiries.
The 65-year-old was arrested on suspicion of the murder on Thursday and held until Saturday night, when he was released on police bail.
Speaking outside the smart Victorian property on Canynge Road where Mr Jefferies lives above the flat Miss Yeates shared with her boyfriend, Chief Superintendent Jon Stratford said: "I can understand why the public in the Clifton and wider Bristol area have concerns for their safety. Whoever killed Jo remains at large.
"However, I want to reassure the public that there remains no specific intelligence or information to suggest there is an increased threat to their safety at this time.
"Naturally we ask the public to continue to take the usual safety precautions. Lone women should avoid walking home alone after dark and householders should keep their premises secure and take care answering the door to strangers."
Increased patrols are being maintained in Clifton to reassure the public, he added, as more than 70 police officers and other staff continue to investigate the brutal crime.
He gave assurances that there was nothing to suggest the murderer was a serial killer.
Mr Stratford also thanked the public for helping with the inquiry so far, revealing that more than 1,000 phone calls had been received.
"We have been overwhelmed with the level of response from members of the public and continue to ask anyone who thinks they may have any information to lead us to Jo's killer to contact us," he said.
He added: "Jo's killer is still out there somewhere and we will find them and bring them to justice. We know Jo was murdered. At the the moment we don't know who killed her but we are determined to find out."
Prayers were said for Miss Yeates yesterday morning at nearby Christ Church, where associate vicar Dan Clark urged the congregation to remember her family, the police investigating the case and the journalists covering it.
He said: "Many of you will know this has been quite a difficult few weeks for the local community following the sad news about Joanna Yeates.
"I would like us to pause and bring our own quiet prayers for Joanna's family."
As the congregation bowed its heads, he added: "As well as praying quietly for Joanna's family, friends and colleagues, let's also pray quietly for the police working hard to solve this case and the press working hard to publicise this case and jog people's memories."