AVA- Five of the dead hostages were members of the same family and included two children, the local mayor, Lielson Landim, told the Folha de Sao Paulo newspaper.
They had been returning from a nearby airport when some of the robbers seized them.
The secretary for security in the state of Ceara, Andre Costa, said in a statement that an investigation was being carried out to identify those killed and the circumstances of their deaths.
Costa did not say whose bullets killed the hostages.
Landim had earlier said that, based on initial information, he understood "the criminals killed the hostages and the police killed the criminals."
Two suspects were arrested, according to Costa's office.
"A heavily armed group arrived in the town in the early hours and went to the center where they tried to commit the crime. There was an exchange of fire between the suspects and police," it said.
It said six gang members were killed and "another six people died from gunshots."
Various weapons and explosives as well as three vehicles used in the bank assaults were recovered.
According to the G1 news website, the robbers had blocked a street with a truck and stopped the car carrying the family, which included relatives who had just arrived on a flight from Sao Paulo to celebrate Christmas with them.
G1 reported that the robbers "executed" the hostages when police turned up. It said some of the gang managed to escape.
Brazil is one of the most violent countries in the world, suffering nearly 64,000 murders last year – a homicide rate of 30.8 per 100,000 inhabitants that is three times higher than the level the United Nations considers to be endemic violence.
On January 1, a far-right politician promising a relentless crackdown on crime, Jair Bolsonaro, will become Brazil's new president following his election in October.
He is known for repeated offensive comments against women, gays and the poor, and for lauding the military dictatorship Brazil shucked off just three decades ago.