The latest discovery was announced by Franco Gabrielli, the head of Italy's civil protection agency, the organisation in charge of the wreck.
"Other remains have also been found and are currently undergoing DNA tests," Mr Gabrielli said.Mr Gabrielli announced last week that, in what was described as "almost a miracle", human remains had been found following the refloating of the 114,500-ton vessel.
Thirty-two people in total died when the ship capsized after striking rocks off close to the island of Giglio, in January last year.
The bodies of 30 victims were recovered but the bodies of an Indian man and an Italian woman were not found.
Experts are planning to go inside the ship to retrieve some of the Concordia's computers, to try to discover why backup generators and other equipment failed to work immediately after the collision.
The ship was hauled upright two weeks ago in a complicated 19-hour salvage operation.
It is due to be towed away from the Mediterranean holiday island, probably by next spring, and eventually broken up for scrap.
The Concordia's captain, Francesco Schettino, is on trial for alleged manslaughter, causing the shipwreck and abandoning ship during a confused and delayed evacuation.
