Mr Gal said the tour boat would be taken on the barge to nearby Csepel Island, where it will be examined by Budapest police as part of their investigation into the crash.
Seven of the 35 people on board were rescued and seven bodies quickly recovered but others were swept away in the swollen river or trapped inside the boat. Seven people were rescued after the nigh-time collision in heavy rain.
Crews have been working for weeks to salvage the Hableany sightseeing boat, which collided with another vessel and capsized in Budapest May 29.
The Mermaid, a Hungarian boat which sank in the Danube River near Margaret Bridge, is lifted from the water during a salvage operation in Budapest, Hungary, on June 11, 2019. South Korean and Hungarian authorities have continued their joint search along the river with divers, helicopters, drones and search dogs.
Those missing include a six-year-old girl as well another captain of the boat.
Several of the victims found before Tuesday were discovered along the Danube, dozens of kilometers south of the Hungarian capital. Mermaid was a 27-metre (89-feet) double-decker river cruise boat with a 150-horsepower engine and had a capacity to hold up to 60 people. Once Hableany is raised from the floor of the river, a joint inspection team of Hungarian and Korean officials plan to search for any bodies that may be inside the vessel. One of the four is believed to be the boat's captain.
On Monday the river cruise boat, the Viking Sigyn, was again searched by Hungarian police who have launched a criminal probe into the cause of the accident.
After the incident, the boat had travelled on to Germany before returning to Hungary according to its schedule.
The captain of the Viking Sigyn, has been under arrest since the beginning of June, suspected of endangering water transport leading to a deadly mass accident.