Mother-of-two Jean Campbell, 53, was last seen walking her dog and heading towards Cranhill Park in the east end of Glasgow last Friday night.
Her body was discovered at around 7.40am the next day by her husband who was out searching for her, after she is said to have suffered a particularly violent assault.
Officers were in the park last night to speak to people and distribute leaflets, appealing for information from anyone who saw Mrs Campbell in the period leading up to her death.
Detective Chief Inspector Colin Carey said: "This is a major investigation with over 40 detectives dedicated to the inquiry.
"So far the response from the public has been encouraging, however, we still have to establish the exact circumstances surrounding Mrs Campbell's death and a motive for her murder.
"It is essential that we piece together Mrs Campbell's last movements.
"We know that she was last seen by a family member around 5pm on Friday night. However, there has been a further confirmed sighting of her in Bellrock Street with her German Shepherd dog Kai around 10.30pm."
Officers have been carrying out extra patrols in the area and have questioned hundreds of local residents.
When last seen, she was wearing pyjama bottoms and a black, three-quarter-length jacket with a hood.
Mr Carey said: "As you will imagine, Mrs Campbell's family are devastated as a result of this loss, particularly in these circumstances and at this time of year when it is especially harrowing.
"If you have any information, no matter how trivial you feel it may be, please contact police."