At least 20 people, mainly South Korean holidaymakers, died following the collision on 29 May. Eight are still understood to be missing.
Footage from the scene near Margit Bridge in the Hungarian capital, near the city’s famous parliament building, showed the stricken vessel being lifted to the surface by a floating crane.
According to the BBC, at least two bodies were recovered from the ship during the recovery efforts on Tuesday morning (11 June).
The ship, Mermaid, was hit by Viking Sigyn at about 9pm local time (7pm GMT) on 29 May after heavy rain saw the river quickly swell.
Reports from the scene at the time of the tragedy suggested the ship sank almost immediately, with some of the passengers swept away by the strong current. Seven were rescued from the river.
One member of the ship’s crew is known to have died, the BBC adds, with the ship’s captain also among the missing.
The captain of Viking Sigyn, a 64-year-old Ukrainian national, has been detained in connection with the incident.