The death toll from flash floods in Kenya's capital Nairobi has risen to 13 after the discovery Thursday of three more bodies, police said.

President William Ruto convened an emergency multi-agency meeting Thursday to respond to the crisis after torrential rains triggered floods that caused chaos across the city, blocking roads and bridges and engulfing homes in slum districts.

Kenyans have been warned to stay on alert, with the forecast for more heavy rains across the country in the coming days.

"We recovered three more bodies today and the search is going on because we have people who were reported missing," local police commander Fred Abuga said.

They were found in the Mathare river that crosses a sprawling slum of the same name which was one of the areas most affected by the floods.

Kenya and other parts of East Africa are vulnerable to climate shocks and the current rainy season has been compounded by the El Nino weather pattern just as the region recovers from the worst drought in four decades.

"We just need to put everybody on alert," Ruto said, adding that those living in the most vulnerable areas would be relocated.

Deputy President Rigathi Gachagua said daily alerts would be issued to the people of Kenya to inform them of the situation.

"The government... will do whatever it takes, apply all the required resources in terms of money and personnel to make sure that lives are not lost and the people of Kenya are protected from this disaster," he told a press briefing.