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Uhuru Kenyatta has pledged that he "will deliver" after it was confirmed he would be installed as the country's new president on April 9.
Violence has erupted after the Supreme Court threw out a legal challenge by the defeated Raila Odinga.
David Cameron has appealed for calm in the country.
Defeated Kenyan presidential candidate Raila Odinga has wished the country's new president and his team well after the Supreme Court threw out his challenge against rival Uhuru Kenyatta.
Writing on Twitter, Mr Odinga said the court process "is yet another milestone on our road towards democracy for which we have fought for so long":
Uhuru Kenyatta will be installed as Kenya's new President on April 9th after the Supreme Court rejected opposition arguments against his recent election.
This will make him the second sitting president in Africa to face charges at the International Criminal Court.
Kenyatta and Deputy President-elect William Ruto deny charges that they helped to orchestrate post election violence in 2007-2008 which killed more than 1,200 people.
Ruto's trial is due to begin in late May while Kenyatta has agreed to report to the Hague in July.
David Cameron has appealed for calm in Kenya after the country's Supreme Court upheld the election of Uhuru Kenyatta as President.
Downing Street has confirmed that the Prime Minister has written to Mr Kenyatta congratulating him for the largely peaceful election.
Opposition supporters were dispersed by police outside the Supreme Court earlier today. Violence following the election in 2007 killed more than 1,200 people following a disputed result.
The defeated presidential candidate Raila Odinga has accepted defeat after the country's Supreme Court threw out his challenge against the victory of rival Uhuru Kenyatta.
Police have fired tear gas at supporters of Mr Odinga who took to the streets of the western city of Kisumu after the result was announced.
Mr Odinga said that he would respect the Supreme Court decision and appealed to his supporters to maintain the peace.
Demonstrations have erupted in Kenya after International Criminal Court-indicted Uhuru Kenyatta was declared the winner of Kenya's presidential election with 50.07% of ballots.
Africa Minister Mark Simmonds said today the UK "greatly values its deep and historic partnership" with Kenya, after the Kenya vote commission confirmed Uhuru Kenyatta as winner of Presidential vote.
Mr Simmonds said that the UK will continue to work with the nation, and that rivals in the election must accept defeat or take their challenge to court. He urged all sides to "show patience and restraint". Mr Simmonds said:
International Criminal Court-indicted Uhuru Kenyatta has said in his presidential speech that he "expects the international community to respect Kenyan sovereignty and democracy", after he won the election today.
Kenya's defeated presidential contender Raila Odinga has said that the election has revealed "serious weaknesses" in the electoral system.
Odinga claimed that there had been 'breaches' in law during the election.
Latest ITV News reports
Ministers pledged to continue working with Kenya after International Criminal Court-indicted Uhuru Kenyatta won the presidential election.