Many high-rise buildings being used for commercial purposes are not properly strengthened, making collapses more likely, he added.
It was not immediately clear how many people were inside when the building foundered.
Kayende said the Lagos state ministry of health was checking with hospitals and once they had finished counting those dead the details would be made public.
An AFP reporter at the scene saw at least eight people pulled from the wreckage, including a small boy with blood on his face.
Residents said there had been a number of building collapses in the area over the last few years.
"We were smoking outside when the building just collapsed", Olamide Nuzbah told AFP in pidgin English.
"Please, save my child, save my child!" wept one traumatised mother whose seven-year-old daughter was trapped inside, as people tried to console her.
"Like we have said, we have been carrying out a lot of integrity tests on the buildings in this neighbourhood and as you can see, some of them have been marked for demolition but we get resistance from landlords but we must continue to save lives and we would intensify our efforts to see that those have failed our integrity test, we would ensure that they are quickly evacuated and we bring the structures down".
On Wednesday, one person was confirmed dead.
NY AG subpoenas Deutsche Bank over Trump business dealings
Olayinka Fadahunsi, Vice President of Communications at Deutsche Bank in NY , declined to comment on the subpoena. To support his testimony, Cohen provided financial statements that he claimed had been sent to Deutsche Bank.
It is not yet known what caused the collapse of the building, which had been earmarked for demolition.
The school was housed in the top floor of a four-story residential apartment building. "If they are doing this they should help us".
Building collapses are tragically common in Lagos and elsewhere in Nigeria, because of the use of sub-standard materials and the non-enforcement of building regulations.
The dilapidated building in the densely populated Lagos Island area of the city came down without warning on Wednesday morning.
Some 84 South Africans were among 115 people killed in 2014 after a guesthouse located within the church of prominent religious leader, TB Joshua, collapsed.
It is characterised by its Afro-Brazilian architecture, a style brought over by thousands of freed slaves who headed back home after decades working the plantations in Brazil.
Dr Hussaini Abdu, Country Director of Plan International Nigeria, called on the Lagos state government to launch an inquiry into the incident. These buildings are not safe.
Two manslaughter prosecutions are now being held in Lagos state after scores of people were killed in two separate building collapses in 2015 and 2016.