The Mermaid boat sank in seconds on 29 May after a large cruise liner struck it from behind under a bridge in the Hungarian capital during heavy rain.
A total of 26 South Korean tourists and two Hungarian crew members died in what was the worst disaster on the river in half a century.
The bodies of all but four of the victims have now been recovered.
One of the bodies was spotted as the captain's cabin came to the surface, a spokesman for Hungary's special forces said.
Further checks will be made in parts of the boat where there could be other victims, the spokesman added.
State news agency MTI reported four victims had been found on Tuesday and recovered by divers.
Salvage crews saluted in respect as each body was removed after divers pulled straps under the sunken boat to allow a huge floating crane to lift it.
The captain of the cruise liner Viking Sigyn - a 64-year-old man identified by police as C Yuriy from Ukraine - is being held over the deadly incident.
His lawyers have said he is devastated and insist he did nothing wrong.
The captain has been questioned on suspicion of misconduct in waterborne traffic leading to mass casualties, according to police.
Swiss-based Viking Cruises Ltd, which owns the Viking Sigyn, has said it is co-operating with Hungarian investigators.
The cruise liner, which left Budapest less than 48 hours after the incident, is back in Hungary on a scheduled trip and docked at the town of Visegrad.
Police said they carried out another inspection on the ship on Monday.