A baby boy and his two-year-old sister were found in the Gibson home on Coleridge Park Drive on Wednesday morning. They were critically injured and rushed to hospital, where they later died.
Although there were reports the children died in the bathtub, police spokesman Const. Eric Hofley said the cause of death is still being determined.
Dozens of people gathered at a vigil Thursday night to mourn the deaths of the children and support the family, including the mom.
The people, many of whom were young mothers, lit candles and sang Amazing Grace on the steps of the Winnipeg Mennonite elementary school, just up the road from the Gibson home in the city's Westwood neighbourhood.
Police said Thursday they believe Gibson is still alive and were urging her to contact them.
Officers were concentrating their search on the family's riverside neighbourhood. Emergency personnel were on the nearby Assiniboine River, and a police helicopter was also being used to look for Gibson.
At the vigil, mourners closed their eyes and joined hands to share a moment of silence, broken by the cries of infants carried by their mothers.
"I came out tonight because I want to support Lisa; if she happens to know that there's this many women and people in general that are not judging her and we're not pointing fingers and we just really want to know that she's OK," said Lisa Burgess, one of the approximately 30 people who attended the vigil.
"To vilify her is not the right thing to do. Our hearts really go out to Lisa and her husband, Brian. We can only imagine how he's feeling right now … and all the people who love them — the friends and family," said Lauren Hope, one of the organizers.
"We're all heartbroken for them."
Many, like Margaret Managh, are trying to find comfort in the wake in what Hope called the "terrible sadness."
"We're really praying that Lisa will be able to come home — if that's to our Creator then that's what it is. If not, I hope she can come home and find some peace," Managh said.