Mend had already given oil companies 48 hours to leave the Niger delta, a deadline that is set to expire at midnight local time (23:00 GMT).
The group warned that all staff and helicopters would be targeted after the deadline.
The military said it was carrying out a "cordon-and-search" operation after the hijacking of two oil vessels and a number of attacks on soldiers.
"The military taskforce cannot just fold its hands and allow these sorts of barbaric events to continue"
Colonel Rabe Abubakar, military spokesman
"The military taskforce cannot just fold its hands and allow these sorts of barbaric events to continue," Colonel Rabe Abubakar, a military spokesman, told the Reuters news agency.
Jonjon Oyeinfie, a Mend activist and former ethnic Ijaw youth leader, told the AFP news agency that "a fierce battle" was raging along the Warri-Forcados river, with the army deploying 13 gunboats and helicopter gunships.
Mend accused the military of using aircraft to bombard civilian targets during the fighting, a charge Abubakar denied.
Edwin Clark, a local ethnic leader, told The Associated Press news agency, that civilians had fled into the bush as the military attacked from the air, water and land.
"The military has declared total war on our people," he said.
The area where the fighting was taking place is home to the Escravos export terminal, operated by US oil giant Chevron, and the Warri refinery, which puts out 125,000 barrels of oil a day.
Violence in the delta has cut Nigeria's oil output by about a fifth since early 2006, forced foreign firms to remove all but essential employees and severely reduced the earnings of the country.
A number of armed groups operate across the region, launching attacks on oil installations and pipelines, as well as abducting oil workers and local officials.
Some are demanding greater autonomy for the impoverished Niger delta or a greater share of oil revenues, while others are criminal gangs kidnapping for profit.