It was learnt that the structure collapsed around 10:00am while class was on.
Children shoes are seen among the ruble of a building collapse in Ita Faji, Lagos.
It's not known how many people lived in the apartments that made up the rest of the complex.
He promised a full investigation once rescue operations were concluded and vowed that those responsible would be prosecuted.
"This incident has further highlighted the urgent need.to take urgent action on issues of safety in schools across the country", country director Hussaini Abdu said.
Local media reported the building houses a school, and more than 40 people were rescued, though it is not yet clear if there are any casualties.
The neighbours ran to the building immediately it collapsed.
Rescue operations are now ongoing with Parents at the scene weeping and calling out the names of their children.
Covered in dust, he was alive but unconscious and appeared to be badly hurt.
NAN correspondent who was at the scene of the incident reports that the building collapsed about 10: am on Wednesday. They promised to do the right thing, but unfortunately, we are hearing of building collapse everyday.
As rescuers worked furiously to reach those inside, distraught parents begged them to find their children.
Adeshida, whose younger sister was the mother of the children, said she was angry because people had complained about the building for the last 12 years.
Scenes of jubilation erupted earlier in the day when a man was brought out alive.
Many locals told AFP that the building, which was in an advanced state of disrepair, had been "earmarked" for demolition by the authorities in Lagos state.
Onlookers crowded around in the densely populated neighborhood in Lagos, Nigeria's commercial capital and a city of some 20 million people.
Building collapses are all too common in Nigeria, where new construction often goes up without regulatory oversight.