"The five men got into a fight in the market, pulled out their guns, and the sound of gunfire was heard around 1:07 p.m.," Susan Cutter, Harris County Sheriff, said.
According to police, two men suspected of being involved in the clash were killed at the scene and three others were taken to separate hospitals with serious injuries. No pedestrians in this market have been injured.
The bomber struck shortly after noon in front of a police recruiting center at Houston.
Investigators say they have a video of parts of the attack, but they are still searching for a video of the conflict.