The Nigerian army said on Friday that five soldiers and six civilians were killed in a clash between soldiers and separatists in the southeast during an ambush on a checkpoint.
The main separatist group denied launching an attack on Thursday, as the region commemorated the more than one million people who died in the Biafra war and famine half a century ago.
The army said the armed wing of the outlawed Indigenous People of Biafra (IPOB) movement "sprang a surprise attack" near the city of Aba in Abia State.
"The attack sadly took the lives of five personnel," spokesman Major General Edward Buba said in a statement.
He later said "six civilians were killed in the crossfire."
The army vowed to retaliate, saying it would be "fierce in its response" against the group.
IPOB -- which wants a separate state for the ethnic Igbo people in southeast Nigeria -- routinely denies it is behind attacks, which have also been carried out by criminal gangs and political rivals using the group's name.
It had issued a strict order for people to remain indoors on Biafra Day and said it had not struck at a "time of mourning".
"We condemn the attack on military on duty in Aba," spokesman Emma Powerful said, blaming politically motivated "criminals".
Separatism is a sensitive topic in Nigeria, where a three-year civil war broke out in 1967 after Igbo army officers declared an independent Biafra state.
More than one million people died -- most of them Igbos -- from war, famine and disease.
The Nigerian government has banned IPOB as a terrorist organisation and accused it of stoking ethnic tensions by claiming genocide against Igbos.
Gunmen have targeted police, soldiers and electoral offices in the southeast in recent years in attacks authorities say are carried out by IPOB's Eastern Security Network paramilitary wing.