Jean Campbell, 53, was last spotted on CCTV at 10.30pm on Friday after leaving her flat in Bellrock Street near Cranhill Park, in the east of the city.
Her body was found in the park by her husband John the next morning, while her German Shepherd dog was later found alive.
Police have stepped up patrols as inquiries continue into what they describe as a "particularly violent" attack.
MSP for Glasgow Provan Paul Martin said officers were working "around the clock".
He said: "Like many people in the East End of Glasgow, I was shock-ed and saddened to learn about the murder of Jean Campbell.
"I have been in contact with local police and they are working around the clock to piece together Mrs Campbell's final movements, which will hopefully lead to the identification and apprehension of her killer.
"I welcome the decision to deploy extra high-visibility patrols in and around Cranhill Park to ease the concerns of residents.
"I will continue to liaise with Glasgow City Council colleagues to consider what steps might be taken to make Cranhill Park a safer place at night."
Mrs Campbell was last seen wearing pyjama bottoms and a black three-quarter length puffer-style jacket with a black hood.
Detective Chief Inspector Colin Carey said the inquiry had "taken on a number of strands, including the seizure of CCTV information and house-to-house inquiries".