The death toll from the collapse of a six-storey building in Kenya's capital has risen to seven and the number of injured stands at 121, police have said.

A rescue operation is continuing to find survivors after the building collapsed in Nairobi's Huruma residential estate late on Friday after days of heavy rains that have left several parts of the city flooded.

"Seven people are confirmed dead and 121 people have been rescued and rushed to various hospitals in Nairobi," Japheth Koome, Nairobi County police chief, told Reuters by phone.

"The search and rescue operation is ongoing for people feared trapped inside the collapsed six-storey building", he added.