However, the initial attempt was unsuccessful as ropes around the fuselage snapped, BBC reported. Four more bodies have been recovered, bringing the total to 69, with more thought to be inside.
Indonesian officials believe the Airbus A320-200 may have climbed too fast to try to avoid a storm and stalled.
The jet was flying from Surabaya in Indonesia to Singapore. The plane's cockpit voice recorder and flight data recorder were found last week.
A preliminary report on the crash is expected to be filed next week, although the full investigation will take months. Divers entered the main section of the fuselage for the first time on Friday.
Poor weather and difficult sea conditions have hampered the salvage operation since the main section of the aircraft was found.
On Saturday, the salvage team tied a lifting bag to the wreckage, which was capable of raising up to 10 tons.
However, seven metres (22ft) from the surface, strong currents and the sharp edges of the emergency door of the aircraft cut the rope connecting the bag to the fuselage.