
In the statement, Mr Stewart condemned the action of the police for violating human rights by using excessive force against protestors.
He further called for the police involved in brutality to be investigated and prosecuted.
"I urge security forces to exercise maximum restraint and call on protestors who are exercising their constitutional rights to do so peacefully. All allegations of abuses on the part of the security forces should be fully investigated and action taken against security personnel found to have committed violations," the statement read in part.
Kenya has been rocked by violence since the country's top court annulled the Aug. 8 presidential elections. The violence has killed at least 50 people and injured several others, according to rights groups in the country.
However, on Thursday, Police stated that they killed four protesters and arrested 80 others since the repeat election date.
Mr Stewart assured that the UK government would support Kenyans during this critical time where the country's democracy was put to test.
"I have followed closely developments in Kenya over the last few days as the elections have taken place. This is an important moment for Kenya and African democracy. The UK stands together with all Kenyans at this critical time," he conveyed.
The UK minister for Africa raised concerns over outbreaks of ethnic and political violence. He urged leaders and politicians to categorically and publicly shun violence and make every effort to ensure their supporters do so as well.
He further called on all Kenyans to come together at this critical moment and participate in an open and transparent national dialogue, to reject the politics of hatred, and to resolve divisions, so that Kenya moves forward towards greater peace and prosperity.
This statement comes after the Independent Electoral and Boundaries Commission (IEBC) having declared Mr Uhuru the winner of the disputed repeat presidential election.