South Wales Police held a special news conference on Wednesday confirming that the search for the mother is ongoing.
It follows the discovery near the junction of Penarth Road and the Taff Embankment after 18:00 BST on Tuesday.
Police said their main focus was to provide "medical and emotional support" to the mother.
A section of the riverbank was sealed off on Tuesday while a detailed search was carried out, involving forensic teams, dogs, firefighters and a police helicopter.
Police said they are not searching the river for the mother and do not believe she entered the water.
They are so far unable to confirm the baby's ethnicity.
Appealing directly to the mother, Det Insp Gareth Morgan said: "I can understand you will have been through a traumatic time and I can reassure you we do have professionals in place with specialist skills who can provide you with support.
"Somewhere in the community there is a female who may be struggling with the after-effects of the birth and subsequent death of their son.
"I'm appealing to the public for any information concerning this incident; in particular those who frequent the Taffs Mead Embankment and those who use the river and may have seen something out of the ordinary between Sunday of last week and yesterday evening."
Police confirmed they are also carrying out house-to-house enquiries and additional patrols in the area to "provide reassurance" to the public.
Neighbours have since spoken of their shock following the incident.
Resident John Pearce Jones said: "It's a very, very quiet area. It was a shock to everybody."
Anna Padesta recalled how she looked outside to see a police helicopter hovering overhead and police tape across the embankment.
"It's awful, really sad. It does make you wonder what the poor mother has been going through to do that," she added.
Anyone with any information is asked to contact South Wales Police on 101.
Police have renewed their appeal to trace the mother of a newborn baby boy whose body was recovered from the River Taff in Cardiff.