The members of MEND - a coalition of groups that have staged a series of kidnappings and attacks on the oil industry in recent months - were involved in the release of a hostage when they claim that they came under fire from government troops.
Government officials often seek the help of such groups to secure the release of hostages and usually tip off security forces to ensure that they do not come under attack.
The gunfight broke out when the group, having taken possession of the hostage - an employee of Royal Dutch Shell - ran into a heavily armed convoy escorting supplies to an oilfield in the Brass Creek area of Bayelsa state.
There are conflicting accounts of what happened, with MEND saying that their boat, carrying the hostage, was ambushed while the military say that their convoy was attacked.
MEND said: "We lost 10 of the 14 fighters in this attack."
A military source said that three soldiers were also injured and that the MEND boat was seized.
It was not clear whether the hostage - a Nigerian community liaison worker - survived the fighting.
Shell said that it had received reports of the clash and that its employee may have been affected.
Shell said in a statement: "We are making efforts to determine what actually happened."
The Shell worker was abducted on August 8 during a routine visit to the village of Letugbene in the presence of Bayelsa state government officials.
A series of kidnappings and violence against the oil industry in the world's eighth largest oil exporter, has shaken the region and forced Shell to reduce output by 500,000 barrels a day or a quarter of Nigerian capacity since February.
MEND, which has failed to follow through on more recent threats to widen its attacks, demands local control over the Niger Delta's huge oil resources.
A variety of different groups have staged another series of kidnappings of oil workers this month, with demands ranging from political issues to ransoms and community development projects from oil companies.
MEND said on Monday that it would put an end to the kidnappings for ransom: "We are resolved to halt hostage takings for ransom in the delta and demanded all communities and persons holding such to release them."
The clash in Bayelsa followed a military crack-down on those responsible for kidnappings and attacks in neighbouring Rivers state, where most of the latest wave of kidnappings have taken place.
Troops arrested about 150 people in a raid on a suspected hideout in a riverside slum on the outskirts of Port Harcourt, the largest city in the delta, over the weekend.
A military spokesman said that about 110 people had already been released and that the "cordon and search" operation would now be extended to other parts of the delta.