The dilapidated building in the densely-populated Lagos Island area suddenly collapsed on Wednesday morning.
The casualty rate was high because the building had over 20 rooms; with about eight people living in a room.
Children are among those trapped after a building collapsed in Lagos, Nigeria's emergency agency says.
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.
He said the agency would collaborate with LASEMA to provide relief materials for the victims as rescue operations come to an end.
"We have rescued about 25 people, some already dead", Ambode said, even though he did not say how many died.
A spokesman for the National Emergency Management Agency's southwest region said many people, including children, were believed to be trapped. An unknown number remained missing.
He declined to give an updated toll of the dead and rescued.
"We have searched all the debris and gotten to the last floor of the building; there are no more survivors", he said.
Scores of families waited anxiously at hospitals in Lagos for updates on their loved ones.
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"They do not deserve to die the way they did".
"Like we have said, we have been carrying out a lot of integrity test on the buildings in this neighbourhood and some of them have been marked for demolition".
A visit by the News Agency of Nigeria correspondent to the General Hospitals in Marina and Gbagada in Lagos, on Thursday, showed that some of the patients had been stabilised, while others were still being attended to.
"Let's thank God for God, he's getting better but his condition is so critical", she said with fear. She didn't finish, though; she was hushed from further speaking to us by other women who restrained from "saying too much".
The cause of the collapse is yet to be ascertained.
Lagos State Governor, Akinwunmi Ambode, said the building, which had been marked for demolition in 2017, was classified as residential and that the school was operating illegally.
A Reuters reporter saw a boy of 10 being pulled from the rubble, covered in dust but with no visible injuries, and the crowd erupted into cheers as another child was pulled out. But the crowd quieted as others were pulled out and slung over people's shoulders, unmoving.
"The building is not technically a school, it is a residential building that was actually accommodating an illegal school, so to speak, on the second floor", he said.Some authorities disputed that, but all grieved.
Nigerian President Muhammadu Buhari on Wednesday said he was saddened by the incident, which mostly affected children.