Bowornmongkol Police, whose jurisdiction covers the pier where the first body part was found, will handle the investigation.
DNA tests will be conducted on the remains to determine if they came from the same person, deputy police spokesman Maj-General Songpol Wattanachai said.
City police have contacted police in Rayong’s Muang district for information after a woman filed a complaint there claiming that her husband was abducted a few days earlier.