(Changes dateline to Geneva, adds detail, quotes) GENEVA, July 3 (Reuters) - Child malnutrition rates are at crisis levels in refugee camps in Kenya, where desperate parents are selling food supplies to get firewood and soap, three United Nations agencies said on Tuesday. In a joint appeal, the U.N. High Commissioner for Refugees (UNHCR), World Food Programme (WFP) and UNICEF asked donors for $32 million to help improve care for children at the Dadaab and Kakuma camps, which house 237,000 refugees, mainly from Somalia and Sudan. Aid shortfalls have meant those living in the camps have received less than 15 percent of the firewood and less than half the amount of soap they need, the agencies said. Many have also faced water shortages. "If refugees don't get firewood, or soap, they have to sell their general food rations to buy it," said WFP deputy country director Marian Read, who estimated that 20 percent of children under the age of five at the camps are now so malnourished they need special care. The United Nations said renewed fighting in Somalia had sent 40,000 people fleeing to Kenya since mid-2006. Cholera, measles, meningitis and Kenya's first case of polio in 20 years have been recorded in the camps over the past year, and malaria is a constant threat, the agencies said. Better-staffed medical facilities were needed in the camps. "The malnutrition crisis that we are witnessing in the refugee camps in Kenya is the cumulative effect of years of recurrent budgetary shortfalls," Eddie Gedalof, UNHCR's acting representative for Kenya, said. Their $32 million appeal would allow them to supply soap, cooking fuel, energy-saving stoves and food, including items rich in micronutrients such as ground nuts, and improve infant-feeding and breast-feeding practices. Those living in the camps are dependent on international aid for their survival, given Kenyan government policies prevent them farming or working outside the sites.