A missing mother who might have given birth near a riverbank has been urged to go to hospital as investigators look for any trace of the woman or her baby.

It has been more than 24 hours since the discovery of a placenta and umbilical cord on the banks of a river in suburban Sydney.

Authorities insist there will be no judgment, appealing for the mother to seek urgent care amid concerns for the health of the pair.

Health Minister Ryan Park said his heart went out to the mother and giving her access to the best possible care was the priority.

“You’re not in trouble, you don’t have to talk to the police, the only thing I ask you do is make your way to one of our hospitals so that we can care for you and your baby as quickly as possible,” he said.

The appeal came after a dog walker discovered a placenta and umbilical cord near the Cooks River at Earlwood, 10km southwest of the city centre, about 4.30pm on Monday.

Forensic testing will probe when and where the birth took place, with detectives unable to rule out the possibility the unidentified mother delivered her baby at the side of the notoriously polluted river.

One line of inquiry is whether the newborn, along with other evidence of the birth, was dumped, although police are yet to find anything to indicate the baby had been harmed.

Police divers and a blood-detection dog were called in on Tuesday morning as part of an ongoing, large-scale search, but the operation was winding down by early in the afternoon.

A site near the riverbank was surrounded in a blue tarpaulin as investigators looked at the possibility material had been buried there.

But a false alarm was declared when police instead discovered a freshly buried cat at the location.

The site where the placenta and cord were found is not far from a sports field and an Islamic centre on Lang Rd, which ends with a busy footbridge across the river.

Superintendent Christine McDonald said the main focus of police was the welfare of the woman and her child.

“Childbirth, for many people, can be a traumatic time, and it can be very distressing … I am deeply concerned for the safety and the mental health of the mother,” she told reporters on Tuesday.

The woman might have given birth and disposed of the placenta and umbilical cord in the river because she did not want anyone to know about the baby, Supt McDonald said.

“There is no judgment, they need to know we are concerned for them,” she said.

The riverside site is less than 4km from Canterbury Hospital and is frequented by walkers, joggers and dog walkers.

One passer-by told AAP the section of riverbank where the birth evidence was discovered was far from a purpose-built walking track.

“There’s not much of a walking track in that area, you can only walk along for about 200m,” the woman said.

“Cooks River is generally a very busy walking area … this area on a Saturday gets pretty crowded and lots of schools come down (to the rugby club) to play cricket, touch footy, that sort of thing.”

The Cooks River flows from Yagoona in Sydney’s outer southwest and runs into Botany Bay at Kyeemagh, 23km away.

Sections are heavily polluted as a result of traffic congestion, litter, sewage, illegal dumping and industrial and domestic activities.

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