The Governor, who came in at exactly 2:45pm, said from the briefing he got from the Lagos State Emergency Management Agency boss, 25 bodies have been rescued so far.
But they had also recovered "more than four dead bodies", Mr Tiamiyu said without giving an exact figure.
He went on to "charge the Lagos State Government to do all that is needful, so that such tragic developments do not recur".
Ambode said the school had been set up illegally and that buildings in the area were undergoing integrity testing.
Two teachers, three adults were clearly stated, while the 36 other victims are assumed to be children.
Both men took to Twitter on Wednesday to sympathise with the victims' families following the incident which occurred at the Ita Faji area of Lagos Island.
Building materials are often sub-standard and the enforcement of regulations in Nigeria is weak.
Hundreds of people stood in narrow streets and on rooftops of rusted, corrugated metal. A yellow excavator scooped at the ruins of rebar and dust. Some were barefoot. Some were bare-handed.
The collapse came as President Muhammadu Buhari, newly elected to a second term, tries to improve groaning, inefficient infrastructure in Africa's most populous nation.
"The perceived quality of the infrastructure is low".
In December 2016, at least 60 people were killed when a roof fell in on a church in Uyo, the capital of Akwa Ibom state, in the east of the country.