"We are troubled by reports that some demonstrations have turned violent, and call on all Kenyans to reject violence and resolve disputes in accordance with the Kenyan Constitution and the rule of law," the release said on Monday.
The United States, the release added, also congratulates the people of Kenya and President Uhuru Kenyatta for holding successful elections.
Earlier, shots were fired and homes were set alight in poor neighborhoods of Kenya’s capital Nairobi after the electoral commission handed the presidential election victory to incumbent Uhuru Kenyatta.
The outbreak of violence has spurred fears of ethnic killings after the 2007 presidential election dispute triggered a political and social crisis that claimed over a thousand of lives and displaced hundreds of thousands.