There have been reports authorities had hoarded the items in order to share with family and friends.
But authorities in Abuja have denied those claims as citizens cart items away on foot or by motorbike.
Hundreds of residents were seen on Monday crossing the city loaded with boxes of food.
In a statement Nigerian governors explained that all food aid had not been distributed because “we have chosen to keep strategic reserves in anticipation of a second wave of coronavirus.”
A looter was quoted by AFP as saying that “We are hungry, you must understand.”
“There is plenty of food in this country, but its people are suffering. The government is kidding us by leaving this food in warehouses.”
According to local media reports almost a third of Nigeria’s 36 states and the capital have seen stores attacked by looters.
There have been reports of deaths, many of the victims crushed as people crowded into the warehouses.
More than 400 people have been arrested in Lagos alone and will be charged, according to authorities.