The statement issued by the office of President Muhammadu Buhari, who previously led Nigeria as a military ruler in the early 1980s, said "a rude shock" awaits "those bent on destroying the country through promoting insurrection, and burning down critical national assets".
It referred to the 1967-70 civil war fought over the secession of an area in Nigeria's far southeast called Biafra that killed one million people.
"Those of us in the fields for 30 months, who went through (that) war, will treat them in the language they understand. We are going to be very hard sooner than later," Buhari, who served in the army against the secessionists, was quoted as saying.
On Monday the streets of towns across the southeast were quiet and businesses were shuttered after the IPOB urged people to stay at home to commemorate those who died in the war.
The presidency statement said there had been 42 attacks on offices of the Independent National Electoral Commission in recent months across 14 states.