* Concordia salvage enters final stage
* Most complex wreck recovery ever attempted
* Bodies of two of the 32 victims have yet to be found (Updates with detail on timing, adds quote)
GIGLIO, Italy, Sept 16 (Reuters) - Salvage crews lifted the wrecked Costa Concordia cruise liner off a rock shelf on Monday as they worked deep into the night to complete one of the most difficult and expensive maritime salvage operations ever undertaken.
The 114,500-ton Concordia has lain half-submerged on its side just off the Italian island of Giglio since it ran aground and sank with the loss of 32 lives on Jan. 13, 2012.
After a day of slow and painstaking work, the ship had been lifted by more than 25 degrees from its original resting place and progress towards bringing it fully upright was expected to take no more than a few hours.
"We have started the final phase of the rotation," Franco Gabrielli, the head of Italy's Civil Protection Authority told reporters. "We are approaching the final phase of the operation," he said, adding that the operation could be complete by 4.00 a.m (0200 GMT).
Work began at 9 a.m. (0700 GMT) after a three-hour delay due to an overnight storm and progress was slower than originally estimated but engineers said the project had matched their expectations fully.
"Everything has gone has gone smoothly, as expected and this last phase should go as safely as possible," said Franco Porcellacchia, leader of Costa Cruise's technical team.
As searchlights lit up the salvage scene in the port of Giglio, the flank of the ship was entirely off the rock shelf and raised far enough out of the sea to reveal a dirty brown water mark staining the white hull.
The Concordia was carrying more than 4,000 people when it hit rocks off Giglio and capsized. Two bodies have yet to be recovered and underwater cameras failed to find any sign of them as darkness fell.
"They must still be under the keel of the Concordia and I hope after this finally they will have a grave (their families)can cry over," said Luciano Castro, a 49-year-old journalist who was on the ship when it sank.
In contrast to the accident, a catalogue of mishap and misjudgement over which the Concordia's captain Francesco Schettino faces multiple charges, the salvage operation has so far been a tightly coordinated engineering feat.
At a cost estimated at more than 600 million euros ($795 million), it is expected to be the most expensive maritime wreck recovery ever, accounting for more than half of an overall insurance loss of more than $1.1 billion.
"I WANT TO SEE IT TAKEN AWAY"
The so-called "parbuckling" operation has seen the 114,500-ton vessel slowly rotated towards an upright position using a series of huge jacks and cables prior to being towed away and broken up for scrap, probably next spring.
A multinational team of 500 salvage engineers has been on Giglio for most of the past year, stabilising the wreck and preparing for the lifting operation, which has never been attempted on such a large vessel in such conditions.
"We have done parbuckling before but never on a location like this," Nick Sloane, the South African engineer coordinating the recovery for contractor Titan Salvage, told Reuters.
"She is on the side of a mountain on the seabed, balanced on two reefs and she is a really large ship - she's three football fields long, a hundred thousand tonnes plus ... So it's never been done on this scale," he said.
A series of 11 towers with hydraulic mechanisms controlling 205-kg (450-lb) cables under the ship and attached to its side slowly rotated the vessel, aiming to place it on six specially built platforms drilled into the granite rock bed.
As the sunken side of the vessel emerged from the water, engineers ceased the pressure from the cables and huge tanks fixed to the ship's exposed side began filling with water, using the effect of gravity to pull the ship vertical.
Oil booms surround the vessel to intercept waste water and oil trapped in the ship, but no significant environmental damage was observed in the first hours of the operation.
Once the Concordia is upright, salvage teams will spend months stabilising it and preparing for it to be re-floated with the aid of additional giant buoyancy tanks before it is towed away for scrap.
Marine insurers who have to calculate the cost of covering a new breed of large cargo and cruise vessels have been watching progress closely, as any problems could have a significant impact on future insurance contracts.
On Giglio, locals were hoping the ship that has given their Tuscan holiday island global fame would soon be gone.
Giancarlo Farni, who said he was one of the first rescuers on the scene, said: "I saw it sink and now I want to see it brought upright and taken away." ($1 = 0.7542 euros) (Additional reporting by Eleanor Biles, Hanna Rantala, Antonio Denti and Cristiano Corvino; Editing by Elizabeth Piper and Eric Walsh)