"The investigation remains open and continues by members of our homicide unit," Const. Eric Hofley told reporters on Sunday.
"There's been a lot of speculation out there in the media and in the public, however investigators have to ensure that every possible avenue has been followed up."
Gibson’s family was requesting privacy, Hofley added.
Gibson, 32, had been missing since Wednesday when her two young children were found in critical condition inside their house. The two-year-old girl and three-month-old baby boy were taken to hospital where they were pronounced dead.
Gibson was the last person to be with the children, police said, but they did not label her a suspect, and would only say they were concerned for her well-being. By Friday, a dive team was searching the Assiniboine River near the family's home. Her body was found Saturday downstream, not far from where the Assiniboine empties into the Red.
There are media reports Gibson suffered from post-partum depression, and that the children were found in a bathtub inside the home.
Police said autopsies have been conducted, but would not release details.
"At this point, the results of those autopsies have to be fully looked at by those investigators to determine if perhaps there are some other explanation as to the cause of this incident," Hofley said.
"It has been speculated that Ms. Gibson is responsible for this, but until all the evidence has come forward, officers need to be aware and not rule out any possibility that perhaps someone else is responsible."
Gibson's open Facebook page, which has since been restricted, was full of happy pictures of her children: Anna, age two, and Nicholas, almost three months old.
The page included a family photo that appeared to be taken at a hospital shortly after the birth of Nicholas in April, along with a proud birth announcement.
The last posting was mid-June — a picture of Anna with the caption reading: "Man I love this kid.''
The page also included a picture of Gibson's husband, Brian, who was not at home at the time of the deaths.
"I can't imagine how Mr. Gibson is doing (at) this point. Certainly, my thoughts are with him," Hofley said.