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Most of the deaths occurred when police opened fire on the robbers at the bank branches on the main street in Milagres in the interior of Ceará state, a statement by the governor's office said.
Five of the alleged gang members died in the night-time shootout shortly after 2 a.m local time, two died in hospital of bullet wounds and an eighth was gunned down in a police pursuit, it said.
Six people who had been taken hostage on a local highway that the gang blocked with a trailer truck also died in the shootout, the statement said. It said three suspects have been arrested by police.
Local media reported that five of the dead hostages were from the same family, including two children aged 14 and 13.
The attempted robbery was interrupted by a police unit that had been tracking a gang responsible for similar bank robberies in the area.