An arm found floating in a Melbourne river has a distinct devil tattoo on it, which police hope will help them identify a series of gruesome remains.

A passer-by found a forearm floating in the river at Moonee Ponds on Thursday afternoon, sparking a large-scale police search of the area.

The arm has a tattoo of a devil holding a three-pronged pitchfork in its left hand, and what appears to be an aerosol can in its right.

Police also found a second limb in the water two kilometres away as well as a bag believed to be full of flesh.

Officers conducted an overnight search around the river and police divers returned to the site on Friday morning.

The body parts are being examined by forensic pathologists.

Detective Inspector Mick Hughes said police released an image of the tattoo in the hope someone would recognise it.

"I think it's important from the family's perspective, we know this is a terrible way for them to find out," he said.

"But I think it will help get a breakthrough in our investigation."

Police said they were treating the discovery of the body as suspicious.

Detective Inspector Hughes said the tattoo was being cross checked with the police missing persons and criminal database.

"Tattoo parlours will also be one avenue we look at as well," he said.

Police believe the remains belong to a man.

Officers are continuing to search a one kilometre stretch of the river where the other body parts were found.