The discovery comes as preliminary operations got under way to remove the half-million gallons of fuel on board before it leaks into the Tuscan sea.
Crews from a Dutch salvage firm were seen on the ship Tuesday morning, and fuel extraction equipment has moved in next to the liner.
Officials say the pumping will start on Saturday and will be carried out while divers continue the search for the missing.
The Concordia ran aground and capsized off the Tuscan island of Giglio on Jan. 13 after the captain veered from his approved course and gashed the ship's hull on a reef, forcing the panicked evacuation of 4,200 passengers and crew.
Of the 16 bodies found, at least six of the badly decomposed bodies remain unidentified, and are presumed to be among some of the 17 passengers and crew still unaccounted for.
The captain, Francesco Schettino, remains under house arrest facing accusations of manslaughter, causing a shipwreck and abandoning the ship before all passengers were off.
The Concordia is a unit of Carnival Corp., the world's biggest cruise operator. Early Tuesday, amid continued outrage by passengers of the chaotic evacuation, the cruise ship's owner promised to refund the full cost of the cruise, reimburse all travel expenses to and from the ship, all on-board expenses and any medical expenses incurred as a result of the grounding.
The Associated Press contributed to this story.