President Uhuru Kenyatta visited the wreck of the six-storey building today, where 10 people perished after concrete floors collapsed down on top of each other during torrential rainstorms yesterday.
The two-year-old building, home to more than over 150 families, had been condemned by building authorities but the order had been ignored.
"Ten bodies have been recovered, and we have 80 people who have been treated and discharged from hospital," Interior Minister Joseph Nkaissery told reporters amid the wreckage of the building.
"There is a lady in the building and her child who are alive, and all efforts are being made to rescue them, as well as other people still believed to be in the building," Nkaissery said.
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But access for rescuers with larger machinery has been made difficult by the narrow and crowded streets.
One survivor was pulled from the huge pile of debris shortly after dawn, Kenya Red Cross said, some 10 hours after the building collapsed last night.
Pictures broadcast by local media showed soldiers, policemen and civilians searching through the rubble.
He ordered police "take immediate action to identify and arrest owners of buildings who have ignored directives by the National Construction Authority", it said.
The building collapsed at around 9:30 pm (1830 GMT) yesterday following some of the heaviest downpours since the start of the rainy season that caused flooding and landslides in many areas of the city.
Two neighbouring buildings were declared unsafe and were evacuated.
In other separate incidents, two people drowned when their vehicle was swept away by storm waters in the capital's Industrial Area, another person died in floods.
The growing middle class has triggered an explosion in demand for housing and a rise in real estate prices in the east African capital.