Dozens of tourists from South Korea were killed alongside two crew members in what was described as the worst disaster in 50 years on the river.
At least two bodies have been recovered from the wreck of a tourist boat that sank on the Danube in the Hungarian capital, Budapest, last month.
Efforts to search for the missing victims of the accident and to raise the Hableany have been hindered by the Danube's high springtime water levels - which are expected to fall significantly over the coming days in Budapest - and the river's fast flow, as well as near-zero visibility under water.
Search operations to find the missing will also continue after the ship is salvaged, Song Shun-keun, a defense attache at the South Korean Embassy in Budapest, said.
The lifting of the vessel from the water is planned in several stages, depending on factors such as the condition of the hull and the discovery of bodies.
Swiss-based Viking Cruises Ltd, which owns the Viking Sigyn, has said it is cooperating with Hungarian investigators.
Those on board included a six-year-old girl travelling with her mother and grandparents, and the Mermaid's Hungarian captain.
At one point, one member of the rescue crew fell into the fast-flowing water and had to be rescued after nearly being swept away.
Before the Mermaid is fully raised, divers will enter the wreck to search for any bodies still trapped inside, officials said.
Criticism arose as it turned out part of the cruise boat has been repainted in an apparent attempt to hide and destroy traces of the collision.
Police have launched an investigation into the cause of the accident and the captain of the river cruise boat which collided, the Viking Sigyn, has been arrested on suspicion of "endangering waterborne traffic resulting in multiple deaths".
Four more bodies were pulled out of the Danube on Tuesday, during the salvage operation.
Nineteen South Koreans and a Hungarian crewman have been confirmed dead, with eight people missing.
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