Teacher Sabina Nessa may have been murdered by a stranger as she took a five-minute walk to meet a friend in a pub, police have said.
The 28-year-old never arrived and was attacked in Cator Park in southeast London.
Giving an update on the police investigation at the scene on Thursday, Detective Chief Superintendent Trevor Lawry said the possibility the primary school teacher was attacked by a stranger is "definitely a line of enquiry that we're looking at".
Her body, which was "off the track that you would normally walk", was found by someone walking their dog, the local policing commander added.
"Significant lines of inquiry" are being followed. Regarding a motive, officers are keeping a "completely open mind", Det Chief Supt Lawry said.
An "extensive crime scene" will remain for the next couple of days, he added.
Asked whether he was worried the killer could attack someone else, he said: "We have lines of inquiry that we're pursuing at the moment.
"It's always a concern that it may happen, but that's not something that we have any intelligence on at this time."
Ms Nessa, who taught at Rushey Green Primary School, left her home in Astell Road, between Eltham and Lewisham, just before 8.30pm last Friday, detectives said.
Her body was found close to the OneSpace community cafe, inside the park, the following day.
She was on her way to The Depot, a pub on Pegler Square in Kidbrooke Village.
"Sabina's journey should have taken just over five minutes but she never made it to her destination," Detective Inspector Joe Garrity said.
"We know the community are rightly shocked by this murder - as are we - and we are using every resource available to us to find the individual responsible."
A post-mortem examination, carried out on Monday, was inconclusive.
Reclaim These Streets, which campaigned on women's safety following the murder of Sarah Everard, said it will hold a vigil in Peglar Square at 7pm on Friday.
Police will be attending, Mr Lawry said, because officers are "part of the community and wish to stand with the community at this time".
Asked whether people should be concerned, he said: "The streets are safe for women - I'd like to reassure the public around that. I'd like to reassure that people should be free to walk around free from fear and my officers will make sure that that can take place."
Mr Garrity appealed for witnesses, saying: "We are incredibly grateful for all of those who have so far come forward and spoken to us but we believe there are still others out there who may have information that could help.
"If you think you saw Sabina or any suspicious behaviour in or around the park on Friday evening please speak to us."
A man in his 40s was arrested on suspicion of murder and released under investigation, police said previously.
The headteacher at Ms Nessa's school, Lisa Williams, said her death is "desperately sad", adding that she was "kind, caring and absolutely dedicated to her pupils".
Boris Johnson's thoughts are with Ms Nessa's family and friends, Downing Street said.
A spokesman for the prime minister said a strategy on violence against women and girls, introduced earlier this year, will "drive long-term change" and "hopefully prevent these crimes".
The mayor of London said violence against women should be treated with the same priority as counter-terrorism.
Sadiq Khan added that he is in "close contact" with the Metropolitan Police and that his "thoughts and prayers are with Sabina Nessa's family".
He described violence against women as an "epidemic" and said it is "really important that people like me, who have not had to live the experiences of women and girls, listen to the experience of women and girls and work with them to have policies that address this awful issue".
Mr Khan added: "It's just awful what happened to Sabina last Friday. When I think of Bibaa Henry, Nicole Smallman, Sarah Everard, it's heart-breaking."
Anyone with information can call the incident room on 0208 721 4266, or Crimestoppers, anonymously, on 0800 555 111.