Ambode said the school had been set up illegally and that buildings in the area had been undergoing structural testing prior to the accident.
Esinlokun, while speaking with journalists, said the Lagos State Government would ensure that victims of the incident are treated free. "It looks like a dream to me", she said.
"We equally told the state government to carry out integrity test on more structures in the area, but due to lack of political will, nothing was done by the government", pointing out that the incessant building collapses being recorded in Lagos Island, is due to the peculiarity of the local developers who are not professionals.
Speaking to journalists after assessment, he said: "The incident is noted and investigations will be launched to forestall future occurences".
Witnesses said almost a dozen students had been pulled from the ruins, but it was not yet clear if any were dead.
Nigeria's president, Muhammadu Buhari said in a statement on Wednesday evening that he was "deeply saddened" by the building collapse.
Seventeen of those rescued were taken to Massey Children Hospital, close to the scene of the tragedy, while others were taken to the Lagos Island General Hospital on Broad Street.
Covered in dust, he was alive but unconscious and appeared to be badly hurt. While many were lucky to reunite with their wards, several others were apprehensive and hopeful that their children would be brought out alive.
"Landlords who convert residential buildings to commercial purposes should be sanctioned".
Onilenla said: "My friend has seven children also trapped in the rubble".More news: Thousands of Australian Gmail users report problems with service
"We cleared it out to see if anyone was still buried below this rubble".
Many locals said that the building, which was in an advanced state of disrepair, had been "earmarked" for demolition by the authorities in Lagos state.
"They were quick to rescue one of the twins, which is Kehinde".
Lagos, which has a population of 20 million people, is made up of a collection of islands.
"Our response units are already here; we are getting additional cranes to be able to go deeper than where we are now to rescue more trapped victims".
Building collapses are frequent in Nigeria, where regulations are poorly enforced and construction materials often substandard.
In September 2014, 116 people died - 84 of them South Africans - when a six-storey guesthouse collapsed at the Lagos church complex of celebrity televangelist TB Joshua.
"LASBCA and other building regulatory authorities alone can not properly monitor to detect when buildings are defective or when illegal constructions are going on, without the support of the residents".
There was also an urgent call for wrappers by rescue worker in order to form a tight rope cord in the absence of actual ropes.
In 2016, more than 100 people were killed when a church came down in the southeast, and in Lagos the same year, a five-storey building collapsed, killing at least 30 people.