Divers entered the boat as a floating crane slowly brought it to the surface.
The Mermaid was carrying South Korean tourists when it was in collision with a cruise ship and capsized, leaving 20 people dead and eight others missing.
High water levels in the Danube have hampered recovery efforts by Hungarian and South Korean teams.
Footage from the scene this morning shows the cabin and upper deck of the boat emerge from the water and divers then carry out a search for victims still trapped inside.
Pumps then removed water from the hull and the rest of the 70-year-old boat was slowly brought to the surface.
The entire operation is expected to take several hours.
The bodies recovered were believed to be those of 3 South Koreans and the Hungarian captain.