Lagos Gov. Akinwuni Ambode, who visited the site hours after the building collapsed, said the school had been set up illegally and buildings in the area had been undergoing structural testing prior to the accident.
A crowd of thousands of people cheered on Wednesday as dust-covered, shocked-looking children were pulled from the rubble.
On Thursday, National Emergency Management Agency official Ibrahim Farinloye told The Associated Press that the workers had reached the foundation of the collapsed building and did not expect to find more people. All we are trying to do is to scale up this rescue operation.
The governor said his Deputy, Dr (Mrs) Oluranti Adebule, had also visited the hospitals where some of the victims rescued had been taken to and assured that the state government would immediately take over the treatment of the victims and foot their entire bill.
According to Xinhua reporters on site, a teacher, trapped with up to 20 pupils under the rubble, called for help, while emergency services were on ground to assist with the rescue operation.
Shopworker Adeniyi Afolabi, who lives nearby, gave the name of the school as the Ohen Nursery and Primary and said there were 144 pupils in attendance on Wednesday.
Most buildings here "are said not to be in very good condition", Sam Olukoya, a Nigeria-based freelance journalist told NPR's Ofeibea Quist-Arcton.
However, the occupants frustrated the demolition.
It was reported one of the children was successfully pulled out of the rubble of the collapsed structure. But both said not all children were at the school because of sports activities.
The elder child, Amoke, died and her younger sister was being treated for head injuries, Adeshida said.
A rescue team removing victims from the collapsed building on Wednesday.
Two rockets fired from Gaza at Tel Aviv area, says Israeli army
Ronen Manelis, the chief Israeli military spokesman, said the army had been caught off guard by Thursday night's rocket barrage. The Home Front Command did not give any special instructions to Israelis and said they could continue to carry on as normal.
One local resident who witnessed the moment of collapse said there was no warning.
Sunday said his family lived on the second floor of the building and he sent his boys to school there so they wouldn't have to travel far.
"This is unfortunate but we will investigate what has happened and also see the punishment for whoever are the culprits".
"It looks like a dream to me".
"The collapsed building had been marked for demolition about three times, but the building regulatory agency has not demolished it".
He also stated that the owner did some renovation two years ago.
The top floor of the building is occupied by a school with about one hundred pupils, while the rest are residential and shops. A nearby building had collapsed, and her children were inside it.
At the Lagos Island hospital, Adedoyin was relieved that her daughter was out of the building, but her thoughts turned to her son Taiwo, whose whereabouts she still did not know.
"It is too big for her to bear".
"Most of the patients came in through General Hospital and Massey Children Hospital from where they were referred to other hospitals, including Lagos State University Teaching Hospital; Mainland General Hospital and General Hospital, Yaba".