Eight people have been killed and scores injured in two separate car bombs at Nigeria's 50th independence anniversary celebration.

Two explosions hit Nigeria's capital Abuja, destroying three cars near a parade attended by President Goodluck Jonathan and other top government officials, marking the 50th anniversary of independence.

Firefighters, security officials and paramedics attended the scene of the blasts. One man at the scene, words rushing out of his mouth in obvious shock, laid the blame on poor security in the lead-up to the event.

"The SSS, the Police the Nigeria Army, the Air Force," he shouted. "The police especially and the State Security Service, they ought to have been here since day before yesterday, they put security surveillance everywhere, where are they, where are they?"

The blasts came an hour after the Movement for the Emancipation of the Niger Delta (MEND), Nigeria's biggest rebel militia, issued an email warning saying it had planted several bombs and telling people to evacuate the area.

Given its warning, the finger of blame will rest heavily on MEND, which has been fighting for years for a greater share of oil revenues from the impoverished Niger Delta, home to Africa's biggest oil and gas industry.