So far, emergency workers had pulled 41 people alive from the rubble, some of them badly injured, he said.
Speaking with newsmen, Ambode said: "I have been told it is an old and illegal building".
Adedoyin raced to the scene, where a small crowd had gathered and a search had begun for survivors among the rubble of the aging three-story building that had given way without warning, trapping residents, pupils and small goods traders inside.
Scenes of jubilation erupted earlier in the day when a man was brought out alive.
He declined to give an updated toll of the dead and the rescued.
Adeshina Tiamiyu, general manager of the Lagos State Emergency Management Agency, said that the agency had recorded one death so far in the disaster, and had rescued almost 50 people.
Rescue efforts are expected to continue into the night as hundreds of anxious people watch an excavator work under floodlights.
The school had more than 100 students, rescue officials said.
"It touches one to lose precious lives in any kind of mishap, particularly those so young and tender", Nigerian President Muhammadu Buhari said.
"It is believed that many people including children are now trapped in the building", said Ibrahmi Farinloye, a spokesperson for the National Emergency Management Agency's southwest region. But the crowd quieted as others were pulled out slung over rescuers' shoulders, unmoving.
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As rescue efforts got underway, hours passed with little luck, most of it owing to the lack of basic equipment such as flashlights to see through bored holes and crevices.
The spokesperson for the Lagos State Emergency Management Agency, Kehinde Adebayo who confirmed the incident, said that emergency officials were already on ground to attend to the situation. An unknown number remain missing.
Building collapses are frequent in Nigeria, where regulations are poorly enforced and construction materials often substandard.
The three storey building located at Number thirty six Massey street, Ita Faji area of Lagos Island came down at about ten o'clock on Wednesday morning.
The South-West Zonal Head of Public Affairs of the Agency, Ibrahim Farinloye said the rescue operation was ongoing as at 8pm.
Outside the hospital where people taken out of the building were taken for treatment, anxious relatives sobbed and ran toward ambulances as they arrived, hoping their loved ones were inside.
Soon after the collapse, local residents started evacuating victims.
"Above all, we must all take appropriate lessons and learn from this sad incident", he said.
It is not yet known what caused the collapse of the building, which stood in a crowded neighbourhood at the heart of Nigeria's commercial capital.
Esinlokun, while speaking with journalists, said the Lagos State Government would ensure that victims of the incident are treated free.