The men reportedly demanded an ambulance to escape; however, this request was not granted.
"We are doing everything possible to preserve the lives of the people," Leon Enrique Cottin, a bank executive, told Venezuelan television channel Globovision, urging the men to give themselves up to authorities.
"We are in real danger. They can kill us. Please help," read a placard placed at one of the branch's windows.
The hostage takers have already freed two elderly people and another pregnant woman on Monday shortly after the crisis began, police told AFP, while more managed to flee.
There are unconfirmed reports that one more person - a bank teller - was released by the hostage takers on Tuesday.
Overnight the men also accepted a package containing nappies and a bottle for a baby among the hostages, local news reported.
The bank is currently surrounded by military and regional police, hostage family members, paramedics and onlookers.