Mend has issued a Sunday deadline for oil firm to pull out of the Niger Delta
A hostage being held by Nigerian oil militants has been killed during a military attack, they have claimed.
The hostage was a Filipino sailor seized from the boat the MV Spirit on Thursday morning, militants said.
An army spokesman has said a militant camp was "torched" in an operation, but denied claims it had bombed a village.
The militants have now declared an "all-out war" on the military as gun battles continued for a third day this week in the southern swamps.
"One hostage has been killed by stray bullets from the Nigerian army who attacked an area they were being held in Delta State," a spokesman for the Movement for the Emancipation of the Niger Delta (Mend) said in a statement.
The group took at least 15 people hostage from two ships in the early hours of Thursday.
In response, Mend says military planes bombarded a village in Delta State, killing women and children.
But the military says it "torched a militant camp" and only killed fighters.
On Friday Mend also claimed to have boarded a warship, captured the crew and set the ship on fire, but navy spokesman Commodore David Nabaiba said the claim was "lies".
It was not possible to verify either side's claims immediately, as travel to the region is restricted.
"Mend is declaring an all-out war in the region and call upon all men of fighting age to enlist for our freedom," spokesman Jomo Gbomo said in an e-mail to journalists.
"Casualties are mostly women, children and the elderly who could not get away quickly into the bush or high sea," he said of the alleged aerial bombardment.
But army spokesman Lt Col Rabe Abubakar denied the claim.
"The only operation today has been a cordon and search operation, which revealed a militant camp, which we torched," he said.
He said he could not give any figures on casualties.
Mend issued a Sunday deadline for oil companies to pull out of the Niger Delta.
The renewed violence between militants and the military's Joint Task Force was expected by analysts after Mend rejected an amnesty offered by the government.
The government has still not officially said the offer is off the table.
Mend is still holding British hostage Matthew Maguire who was seized from an oil services boat in September last year. His colleague Robin Hughes was freed in April.
Militant groups in the Niger Delta have flourished amid a lack of governance and rule of law.
They claim to be fighting to help local people benefit from the region's oil wealth but fund their activities with oil theft, extortion and kidnapping.
The Joint Task Force, charged with bringing security to the Delta, is accused of brutality and corruption.