The Kenya Meteorological Department has warned of heavy rainfall in five regions from Tuesday.
The agency's Director-General Stella Aura said Western, Central region including Nairobi, northeastern, northwestern and the coastal region will experience torrential rains.
"The heavy rainfall of more than 30mm in 24 hours which is being experienced over several parts of the country is expected to continue," she said.
The intensity of the rains in Western and central regions including Nairobi, she said, is expected to "progressively increase to 40mm in 24 hours between Thursday and Friday this week.
At least 12 people had been killed by Monday, following mudslide occasioned by heavy rains in West Pokot and Elgeyo Marakwet counties where 4,000 people were displaced.
Rift Valley Regional Commissioner George Natembeya said more than 20 people were still missing.
The Met department said Kwale, Kilifi, Mombasa, Lamu, Tana-River, Wajir, Marsabit, Taita Taveta, Nairobi, Nyeri, Kiambu, Nyandarua, Murang'a, Embu, Meru, Kirinyanga, Tharaka Nithi, Isiolo, Samburu, Turkana, Machakos, Kitui were likely to be affected by rains.
Others are Makueni, Garissa, Busia, Kisii, Nyamira, Kericho, Bomet, Nakuru, Narok, Migori, Trans Nzoia, Nandi, Baringo, Uasin Gishu, Vihiga, Bungoma, Homa Bay, Kisumu, Siaya, Kakamega and Nakuru.
President Uhuru Kenyatta has already ordered the Interior Ministry to cordinate the evacuation of locals, for movement to higher grounds to avert another crisis in the area.
On Monday, the ministry sent out a Cable to all County Commissioners to cordinate efforts of moving people to higher grounds.
Areas targetted include Elgeyo Marakwet, West Pokot, Murang'a and Taita Taveta, officials said.
And since Sunday, Kenya Air Force has been airlifting relief supplies to the affected people to help alleviate their suffering in the humanitarian crisis.
"We are putting our heads together and organising ourselves to deal with a clearly impending challenge," Interior Cabinet Secretary Fred Matiang'i said Monday at a joint press briefing with Cabinet colleagues from Devolution, Environment and Energy, "we are working jointly to see how we can effectively support the Kenyans camping in schools and other facilities to avoid the negative consequences of the rains."
Environment Cabinet Secretary, Keriako Tobiko appealed to the public to heed to the metrological department's advisory on climatic changes in order to save lives and property.
Devolution Cabinet Secretary Eugene Wamalwa also urged all governors to play their role in preventing and containing such disasters, while assuring that the government was ready to support the affected families with food and other basic needs.
Energy Cabinet Secretary Charles Keter said that all dams in the country are full at maximum capacity due to the torrential rains.
"In the next two days, those people living in the lower parts of Garissa and Tana River must move to the safest surfaces as soon as possible because there will be flooding," Keter warned.