Twenty-six South Korean tourists and two Hungarian crew died in the worst disaster on the river in half a century. Only seven people were rescued.
Jasenszky said divers would search the boat for any bodies in the hull once it was close to the surface and inspect the wreck's condition.
Korean and Hungarian search teams completed final checks of the pleasure boat that sank in the Danube River in Budapest late last month with 33 Korean passengers on board. The incident, which took place nearly 2 weeks ago, led to at least 20 deaths. and eight people still missing.
The bereaved families of four victims arrived at Incheon International Airport in the morning, while holding the boxes of the victims' ashes, the sources said, adding that their cremation took place in Hungary.
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Four body bags were seen being carried away from the partially raised boat as workers saluted in respect.
Separately, a South Korean woman is missing after she reportedly went overboard from a cruise ship in the Mediterranean Sea.
Hungary's special forces oversaw the operation to bring the wreck of the Hableany to the surface of the River Danube in Budapest on Tuesday.
South Korean President Moon Jae-in said his government would co-operate with Hungarian authorities "to thoroughly investigate the incident". It is not known how strong the hull of the 70-year-old boat is following the collision, salvage experts say.
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(Balazs Mohai/MTI via AP) Rescuers rest on a huge floating crane under the Margit bridge, where the Hableany sightseeing boat sank after colliding with a much larger river cruise ship in Budapest, Hungary, on June 11, 2019.
Seven South Koreans were rescued after the nighttime collision May 29 amid heavy rain.
Rescue officials said Sunday that preparations for the lift, including divers installing four wire harnesses under the Hableany (Mermaid), were almost complete, with some technical and security details pending.
Preparations for taking the boat from the river are expected to be finished by the end of the day, while the actual operation may begin in the evening.
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