When quizzed on the allegation of human rights abuse against the Nigerian Army by the Amnesty International, the Prime Minister said she had raised the issue with president Buhari, adding that she welcomed his decision to establish an inquiry to examine the allegations.
Britain needs to find new economic partners before it confronts the full impact of exiting the European Union, he said.
The UK is to increase its military support to Nigeria to help protect its citizens and British workers in the country from terror attacks.
The leaders agreed to strengthen security cooperation - with British soldiers regularly training in Kenya - and to ensure that proceeds of Kenyan corruption stashed in British banks would be repatriated to Kenya.
Ms May is trying to refashion the relationship between the United Kingdom and Africa from one of aid and handouts to a more equal partnership, said Phil Clark, of the School of Oriental and African Studies in London. The government's private equity arm, the CDC group, invested $140 million in ARM Cement, a Kenyan firm, two years ago that was put in administration this month. The returned money will be used exclusively for development projects.
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"We need to make it painfully unrewarding, and expensive to get into corruption", he said at State House, Nairobi, following bilateral talks with Mrs May.
Concerns about the readiness of Somali troops to take over the country's security, however, remain high.
"We are appealing to President Uhuru Kenyatta to request the British government to open our miraa market (sic)", said former Igembe North MP Joseph M'Eruaki, adding that people in Nyambene no longer earn a decent living from miraa sales.
As an African-born British businessman with roots in East Africa, I am delighted that Mrs May is visiting the continent for the first time as the British premier at what is a pivotal moment in the UK's economic future.
On the same note, the article made mention of the fact that Margaret Thatcher had been the last sitting premier to visit Kenya in 1988 claiming that since then, despite historic links between the two countries, the East African country has increasingly turned to China and the U.S. for support and investment.