The men who died were attempting to free a hostage, but were attacked by the Nigerian military on Sunday night on Brass Creek in the southern state of Bayelsa.
The hostage, a Nigerian employee of Royal Dutch Shell, was also killed in the fighting.
In an email to Reuters, the Movement for the Emancipation of the Niger Delta (MEND) said: "Our response to Sunday's killings will come at our time, but for certain it will not go unpunished.
"It was an unprovoked attack on people on a peaceful mission to free a hostage."
State government officials frequently seek the help of MEND activists to secure the release of hostages, and usually tip off security forces of any such operation to ensure that they are not attacked.
The defence ministry expressed "deep regret" on Thursday for the incident and started an investigation.
MEND said it wanted to put an end to a string of kidnappings in the delta this month during which 17 oil workers were abducted in seven separate incidents.
All but one have now been released.
Attacks on pipelines resulted in
a reduction in output
"The reason we decided to put a stop to this is the involvement of criminal elements who have no connection with our struggle," MEND said.
Like many delta militant groups before it, MEND is pressing for more regional control over its oil wealth, compensation for oil spills and the release of detained leaders from the region.
But most of the kidnappings were done by armed "freelancers" seeking ransoms.
MEND's attacks in February forced Shell to reduce output by 500,000 barrels a day, a quarter of the nation's capacity.
But there has been a lull since an attack on a gas plant in June.
MEND has been threatening more violence, and on Thursday reiterated its aim to halt oil exports completely.
"The problems of the delta will only be addressed when we put a total halt to Nigerian oil exports," MEND said, giving no time frame.
Despite the rhetoric, some interpret the lull in attacks as a signal that MEND is giving the government a chance to respond.
Olusegun Obasanjo, the president, set up a committee in April to develop jobs and infrastructure in the neglected region, but the initiative has so far failed to impress activists.
Obasanjo's initiative to develop
jobs has failed to impress
"There has been a lull in vandalisation of pipelines because we are saying let's give the federal government a chance," said Kimse Okoko, president of the Ijaw National Congress.
"It will be difficult to stop the struggle if the federal government refuses to take action."
In an apparent U-turn, Obasanjo last week launched a military crackdown against what he called criminals engaged in kidnapping in the delta, and troops have been combing suspected militant hideouts around the delta city of Port Harcourt.
Activists fear that this, along with Sunday's killings, could mark a resurgence of armed conflict between MEND and thousands of troops deployed to protect oil installations in the vast wetlands region.