At least 14 people have died in Kenya's north-western Turkana region - the first hunger-related Kenyan deaths in the current regional drought.
The MP for Turkana, John Munyes, said the deaths were in three remote villages after the government failed to transport food to drought victims.
The UN says more than four million Kenyans are threatened by starvation in the region's worst drought in 60 years.
Other countries affected are Somalia, Ethiopia and Djibouti.
The BBC's Odhiambo Joseph in Turkana says he visited a village where hundreds of people - most of them old and weak - were queuing for food.
The 14 people who died were Kenyan adults, but children are also severely malnourished, our reporter says.
'People feel abandoned'
Mr Munyes, who is the labour minister in Kenya's coalition government, said the death toll would have been higher if the Red Cross was not distributing aid in Turkana.
"It would have been a disaster," he said.
Mr Munyes said the deaths were not caused by a shortage of food, but by a "lack of logistics".
The government had failed to transport food to villages, he said.
Our reporter says many people in Turkana feel abandoned and are appealing to the international community to pay more attention to their plight.
The UN says the drought has been caused by a lack of rains for successive years.
It has declared a famine in parts of Somalia, which is worst affected.
About 1,300 Somalis - mostly women and children - are crossing into Kenya each day in search of food, the UN says.
On Thursday, the UN's Food Security and Nutrition Analysis Unit (FSNAU) said that famine was "likely to persist until at least December 2011".
On Thursday, US Secretary of State Hillary Clinton called on the militants to let the aid through in Somalia.
"Al-Shabab are preventing assistance to the most vulnerable populations in Somalia," she said.
"I call on al-Shabab to allow assistance to be delivered in an absolutely unfettered way throughout the area... so that as many lives as possible can be saved."
Some 3.2 million people in Somalia are in need of immediate life-saving assistance - almost half the population, the UN says.