Clyde Marshall, 36, of New Brunswick and Sabrina Chouart, 27, of Gatineau, Que. are wanted for first-degree murder in Parsi's death. Mahoney said there have been unconfirmed sightings of the pair, who also have a large dog, in eastern and northern Ontario.
Winnipeg police, meanwhile, tweeted a public warning Monday afternoon that Marshall and Chouart could be in the area.
Mahoney said he believes the suspects may be hitch-hiking and warned anyone who spots them to not approach them.
"You have to be cautious around these individuals," he said.
Parsi, 32, went missing last week after a soccer game. Clues turned up by York Regional Police — who initially treated the Vaughan, Ont. man's disappearance as a missing persons case — led police to Marshall and Chouart's eighth-floor apartment at 230 Woolner Avenue, near Jane Street and St. Clair Avenue West in central Toronto, where Parsi's body was found.
Mahoney did not release the cause of Parsi's death, but said its considered a "violent offence murder."
The homicide detective also declined to say how Parsi knew the two suspects or what he was doing in suspects' apartment, where the pair had lived for around two years.
The two suspects fled the apartment at 4:10 a.m. last Wednesday morning, Mahoney said, leaving Parsi's body behind.
Mahoney said it's possible the pair are still wearing the same clothing — he in a black hoodie with large red design on the chest, her in a bright blue jacket — they were wearing in the video.
The "number one goal" for police, Mahoney said, is to apprehend the suspects.
Anyone with information about the case is being asked to contact police at 416-808-7400, or contact Crime Stoppers anonymously at 416-222-TIPS.