Divers have been searching the area around the ship that became uncovered following the successful operation to right the ship last week.
Two people -- Italian passenger Maria Grazia Tricarichi and Indian crewmember Russel Rebello -- have so far been unaccounted for since the ship ran aground on January 13 last year. Thirty other passengers were also killed in the disaster.
Italy's civil protection commissioner Franco Gabrielli said: "During a search in the water near the central part of the ship, coast guard and police divers found remains which still have to be identified with DNA."
Divers found the remains lying just outside the hull on the seabed this morning near the center of the ship, Italian news agency ANSA reported. The remains have not been brought ashore, but relatives of the two missing people have been informed of the find.
Costa Cruises declined to comment.
Judges approved a move by Italian lawyers representing Captain Francisco Schettino at his trial -- which restarted last week -- for a further investigation of the wreck now that it has been brought upright.
--by Adam Coulter, U.K. Editor