Examinations have revealed that the child was aged up to six weeks old.
Police are yet to identify the infant and officers are continuing to search the area of Restalrig Path, where the grim discovery was made by a dog walker on Sunday.
Detective Chief Inspector David McLaren, from Police Scotland, is leading the inquiry. He said: “Examinations on the remains have confirmed that the remains are those of a newborn baby boy, who may have been up to six weeks old.
“At this time our priority is to trace the mother of the child, who is likely to be in need of medical and emotional support. I want to reassure her that we have her best interests at heart, and encourage her to make contact with us.
“Inquiries are ongoing at Restalrig Path, and the section of the path where the remains were discovered will remain closed as this activity continues.
“I would like to reiterate my appeal to members of the public to come forward with any information that can assist our inquiries.
“The area where the discovery was made is popular with dog walkers and cyclists, and I would urge anyone who has used Restalrig Path in the last month, who has noticed anything suspicious or unusual there, to get in touch with us.”
Anyone with information should contact Police Scotland on 101, or make an anonymous report through Crimestoppers on 0800 555 111.