A 33-year-old woman delivered the infants in Oppenheimer Park on Wednesday night, with assistance from policemen who were on hand for the demolition of a nearby building.
Vancouver Police Chief Jim Chu says the mother suffers from serious mental illness and officers had to step in to save the first baby.
"She was holding the child tightly by the neck and the head, the legs were dangling," he said on Friday.
"They approached her, offered to help and suggested she might want to go to the hospital. She shouted her refusal," Chu added.
Worried for the safety of the baby, and seeing that a second was being born, Chu says police intervened.
"The officers moved in, two of them stood behind her and held her arms, grabbed her fingers, two other officers moved in from the front, put their hands underneath the mother and scooped up the babies and were able to grab the babies as the mother's grip was released from the babies' heads," he said.
The premature babies, a girl and a boy who weighed approximately 3.5 lbs and 4 lbs, have been placed in the care of the Ministry of Family, Children and Community Services.