"The two Spaniards are still missing. We are continuing the search with the army, police and rescue services involved," Indonesia's national disaster agency said on Thursday.
The vessel was carrying 25 people between the Indonesian islands of Lombok and Komodo, famous for its giant lizard species — the Komodo dragon.
Fifteen out of the 25 passengers on board were tourists from Germany,England, New Zealand, Holland, France and Spain. The other ten were Indonesian citizens.
Two Spaniards were rescued from the vessel with one of the survivors telling Spanish daily ABC how they managed to overcome cold, hunger, cramps, exhaustion and jellyfish before being rescued.
It was one of those survivors who said first said two other Spanish people were on board the tourist vessel.
Spain's foreign ministry have now confirmed one of those was Víctor García Montes, a 43-year-old solicitor from Seville, according to Spanish national daily El Mundo.
The other passenger's name has only been given as Jorge.
Some of the survivors said the pair had jumped into the water in an attempt to swim to a nearby island. The two men have not been seen since.
Several of family members of Montes have now gone to Indonesia to assist in search efforts, El Mundo reported.