Seven civilians also died in the crossfire near the Borokiri police station, and a security guard was killed at the Presidential Hotel when armed men opened fire on the lobby, Felix Ogbaudu, local police commissioner was quoted as saying by the state news agency.
Several other civilians were wounded in the attack on the hotel shortly after midnight, and the Skippers night club was also targeted.
A prominent militia leader in Port Harcourt, Ateke Tom, had been expected to stage a counter-attack in the city after troops bombed his suspected hideouts in the creeks around the city last weekend.
Authorities have not provided details on casualties from those raids, but local media have reported that several people were killed.
Violence has driven thousands of foreign oil workers from the Niger delta since armed groups launched a new wave of attacks two years ago.
They have cut oil exports by a fifth and chased away new investment from Africa's biggest oil and gas reserves.
There was a lull for about four months after the inauguration of President Umaru Yar'Adua in May, when the new government began tentative peace talks.
However rebel groups pulled out and resumed attacks after the arrest of one of their leaders in September.
Several armed groups in the delta demand greater local access to oil revenues, an end to what they see as neglect of their impoverished communities, compensation from oil companies for pollution, and greater political autonomy.