It's the second major gun battle between troops and rebels in Nigeria in four days.
The killing follows the kidnapping of seven foreign workers from a US company compound on Wednesday.
The militants called the Movement for the Emancipation of Niger Delta have warned oil facility operators to evacuate the restive region.
The MEND said its units in Rivers State were attacked by nine gunboats and one helicopter gunship of the Nigerian Army.
The group said that it was being "forced" to act ahead of its planned major strike on the nation's oil industry.
It warned that it would not reverse a decision to take hostages in attacks on oil installations.
The MEND had threatened to launch strategic attacks on targets of relevance from Wednesday.
The militants added that the severity of the attacks would depend on the response from the Nigerian military.
Series of attacks
On Monday, about 70 armed men attacked a site belonging to the Royal Dutch Shell company in Rivers State.
Fourteen soldiers were killed and 25 workers were kidnapped but later released.
Seven expatriate workers were kidnapped late Tuesday by an armed group in the region.
Around 60 people, mostly exaptriate oil workers, have been kidnapped, and later released since the beginning of this year when militants stepped up their action in the region.
If MEND's latest claim of killing Nigerian soldiers proves true, the number of soldiers killed since Monday would total 23.
The Nigerian military has not yet indicated how it is going to react to the recent onslaught of the militants.
Troop deployment
In August President Olusegun Obasanjo ordered that troops be deployed to the Niger Delta to do battle with militants following a wave of kidnappings and killings and other forms of brigandage in the region, especially against oil workers.
The militants said that they are fighting for a larger share of the oil
revenues and for the release of their leader, Mujahid Dokubo Asari, detained since last year on treason charges.
They also accuse the government of not fulfilling its promise to provide thousands of jobs and social infrastructure, including roads, water and electricity.
Oil price spike
Nigeria is the world’s eighth largest oil exporter.
Oil prices jumped on news of the fighting with New York crude
futures closing 77 cents higher at 59 dollars 45 US a barrel.
The fighting took place around an oil pumping station at Ekulama
operated by Royal Dutch Shell.
The facility pumps out about 70 thousand barrels per day of crude oil.
Nigeria derives more than 95 percent of its foreign exchange earnings from oil.