As he prepared to board Air Force One in Morristown, New Jersey, on Sunday, Trump told reporters there were "violent people" in Los Angeles "and they're not gonna get away with it".
The alleged rape is the latest allegation of misconduct made against British soldiers at Batuk, which is near the town of Nanyuki around 200km (125 miles) north of Kenya's capital, Nairobi.A MoD spokesperson said: "We can confirm the arrest of a British service person in Kenya in relation to a report of a sexual offence. The service person has been repatriated to the UK and the victim is a British adult, not a Kenyan.
"The matter is the subject of an ongoing investigation by the UK Defence Serious Crime Command, in accordance with the Defence Co-operation Agreement between the UK and Kenya and we will not comment further."A UK soldier has previously been accused of murdering a local woman, Agnes Wanjiru, whose body was found dumped in a septic tank in 2012.The UK has said it is co-operating with a Kenyan investigation into her death.
The Batuk base was established in 1964 shortly after the East African nation gained independence from the UK.The UK military has an agreement with Kenya under which it can deploy up to six army battalions a year for periods of training at the site.
But the British army has faced a string of allegations about the conduct of some UK personnel at the camp.
A public inquiry set up by Kenyan MPs last year heard details of alleged mistreatment of local people by British soldiers.It did not provide numbers as to how many arrests led to charges, convictions or deportations.
It said immigration enforcement officials had "intensified" their work to "tackle those abusing the UK immigration system and exploiting vulnerable people".Officers had visited more than 9,000 businesses - among them restaurants, nail bars and construction sites - to check paperwork and working conditions.
Such businesses had often subjected migrants to "squalid conditions and illegal working hours" as well as below-minimum wages.The Home Office said there were a range of industries exploiting migrant workers.