"The remains were found stuffed in a suitcase and two bags which were found abandoned in S7 and S8 compartments of Hirakud Express which arrived here in the wee hours from Amritsar", said a GRP officer.
He said the victim appears to be a middle-aged male and could have been murdered in neighbouring Orissa.
According to police, the incident came to light after sanitary staff spotted the unclaimed luggage in the two compartments in the wee hours.
The train terminates at Visakhapatnam and the compartments were empty when the bags were found, they said.
The remains are sent to King George Hospital here for postmortem, police said, adding further investigations are on.