Giglio Island, September 16 - The Costa Concordia cruise ship on Monday was successfully freed from the rock reef where it lay in what was considered the most delicate phase of righting the massive wreck in preparation for hauling it away. "The first two hours (of the operation) were the most uncertain, because we didn't know precisely how much of the ship was stuck," said Sergio Girotto, project manager with Italian off-shore engineering company Micoperi, which is in charge of the salvage operation along with US-based Titan Salvage. Girotto described the ship as now being perched on its "knees", meaning that it was placed on a levelled piece of seabed. The righting operation could last until around midnight, meaning it would take hours before anyone could "rest easy," Italy's Civil Protection chief Franco Gabrielli said with a smile on Monday. Gabrielli on Thursday called righting the capsized Costa Concordia "the first (undertaking) of its kind". At 60,000 tons, the water-logged ship is the biggest and most expensive salvage operation in history. No one is certain the unprecedented plan will work given the 15-story, 4,000-passenger vessel's massive size - twice that of the Titanic. Crews have effectively welded a new ship onto the wreckage, attaching 30 giant steel pontoons to its sides to roll the ship in one piece onto a 1,000-ton underwater platform in a process known as parbuckling. Then they will float it away to be cut up for scrap, a process that could take two years. On Giglio Island, off the coast of Tuscany, the cruise ship hit a rock formation in January 2012, claiming 32 lives, after an allegedly rash manoeuvre by Captain Francesco Schettino to "salute" local people. The ship's carcass has since been semi-submerged on its side, with two bodies still missing - passenger Maria Grazia Trecarichi and crewmember Russel Rebelli. Gabrielli called finding those bodies "a priority", but an operation that can only be done once the ship is stabilized and safe. Salvage costs have already reached 600 million euros, exceeding initial estimates by 200 million, even without factoring in the final costs of hauling away the wreckage, scheduled for the spring at the earliest.