A photographer working for Reuters news agency said he counted about 500 corpses, many burnt beyond recognition.
Hundreds of people went to scoop fuel from the pipeline after thieves punctured it overnight at Abule Egba, a heavily populated area, Orebiyi said.
Another Red Cross volunteer at the scene said: "A lot of people have been roasted. They are littered on the ground."
Local television stations ran messages advising the residents living in neighbourhoods close to the blast site to leave.
Those who were burned were taken to hospital in Ikeja, another northern suburb.
Explosions at oil pipelines, often causing large numbers of casualties, are not uncommon in oil-rich Nigeria.
In October 1998, a pipeline explosion killed 1,082 people and injured hundreds more at Jesse in the Niger Delta, and 300 were killed in July 2000 in the same area.