The shooting happened at about 11 am (local time) as troops in a speedboat were patrolling the creeks in Abonnema, west of the Rivers state capital, Port Harcourt.
Army spokesman Captain Eli Lazarus in Port Harcourt described the clash as a "fierce encounter with a group of unknown gunmen suspected to be sea pirates".
"Our men displayed extraordinary gallantry. Unfortunately, an officer and a soldier who sustained various degrees of injury during the encounter lost their lives," he added in a statement.
Rivers and the Niger Delta region were plagued in the 2000s by rebels who attacked oil pipelines and kidnapped workers as part of a campaign for a fairer share of crude revenues.
The region's maze of creeks and tributaries have also been used by maritime pirates who attack ships and take hostages off the Gulf of Guinea.
But the Peoples Democratic Party (PDP) blamed the shooting on "thugs" from the All Progressives Congress (APC) who were "in the process of hijacking election materials", it wrote on Twitter.
The PDP controls Rivers but is in opposition to the APC nationally.
The re-run for seats in the Rivers state assembly and the national assembly in Abuja comes after court rulings on challenges to the initial results.
President Muhammadu Buhari on Tuesday said "violence in any form will no longer be tolerated before, during or after elections", calling political unrest "primitive, barbaric and unacceptable".
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