One of those killed was a one-day-old baby, rescue workers said, as hopes faded for as many as eight people feared to be beneath the smoking piles of rubble from the block of flats that collapsed yesterday evening in Nairobi's Haruma neighbourhood.
The Kenyan Red Cross said four people had died and 40 were injured in the collapse.
President Uhuru Kenyatta warned builders they would face criminal charges if they flouted rules as he condemned a "proliferation of impunity" by developers ignoring "basic laws and regulations."
"We don't have enough machines that will help," said Pius Mwachi from the government's national disaster centre.
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Corrine Torre, from Doctors Without Borders, said rescuers were working as fast as they could.
"If they don't go slowly everything can fall down and it would be a big mess, but after 24 hours we are not very confident" of finding survivors, Torre told AFP, adding that the baby killed had been born only the day before.
He also said the upper floors were built in quick succession, putting pressure on the lower floors, and added that the construction had not been permitted by local authorities.
"The fault lies with the developer... Responsibility starts with the individual," Odongo said.
Large numbers of people flocked to the scene, some helping to dig away the rubble with their bare hands, although crowds were pushed away by police as heavy lifting machinery and official rescue teams were brought in.