Residents said most of the victims were bystanders.
The official News Agency of Nigeria (NAN) reported that fighters had thrown dynamite at a radio station run by the Rivers state government.
Gang members also set fire a large fuel station in the city.
"We heard gunshots and dynamite blasts during the night and it went on for hours, " said a resident of the Lagos Bus Stop area.
Mike Okiro, the Nigerian police chief, said ahead of a meeting with the governor of Rivers state and the local army commander that authorities planned to "clamp down" on the gangs.
The exact cause of the eruption of violence on Monday is unknown, but residents said they believed the fighters were drawn from two of the city's larger gangs who are rivals in criminal activities in Port Harcourt.
Violence escalated in early 2006 in the vast Niger Delta oil region when armed groups demanding greater regional control over oil revenues and an end to neglect by politicians started blowing up pipelines and oil wells as well as kidnapping foreign workers.
Since then criminal gangs have moved into kidnapping for ransom. Armed robberies have also increased.