The body of 21-year-old Agnes Wanjiru was found in a septic tank at the Lions Court Hotel in the town of Nanyuki, close to a British Army training camp, two months after she disappeared in March 2012.
The head of the Army has said he is "appalled" by claims British soldiers were involved in the killing of a young Kenyan woman whose body was found in a septic tank.
The body of 21-year-old Agnes Wanjiru was found at the Lions Court Hotel in the town of Nanyuki, close to the Batuk (British Army Training Unit Kenya) camp, two months after she disappeared in March 2012.
Sky News reported exclusively on her death at the time, with sources claiming they had seen Ms Wanjiru arriving at the hotel with British soldiers on 31 March that year.
According to a report by the The Sunday Times, a soldier accused of the murder has been named by his comrades after he allegedly confessed to the killing.
In a statement, General Sir Mark Carleton-Smith wrote: "I am sure you are all as appalled as I am at the recent allegations surrounding the murder of Agnes Wanjiru in Nanyuki, Kenya, in 2012."
He added: "I want you to know I am determined we support the appropriate authorities to establish the facts of the issue as quickly as possible."
The paper said another soldier reported the killing to senior officers at the time, but no action was taken.
Sources have previously confirmed to Sky News that the UK government had been aware of the incident and the accusations.
A post-mortem examination found Ms Wanjiru died as a result of stab wounds to her chest and abdomen.
There was also evidence she had been beaten, although due to the condition of her body it was unclear whether she had been sexually assaulted.
Witnesses told The Sunday Times that Ms Wanjiru, a sex worker, was last seen leaving the hotel's bar with a British soldier.
Speaking exclusively to Sky News at the time, the police chief said his detectives were actively investigating allegations that two British soldiers murdered Ms Wanjiru.
Joshua Lutukai dismissed suggestions his force was not investigating the crime rigorously enough.
The initial inquiry stalled, but a fresh investigation was launched after an inquest delayed until 2019 found Ms Wanjiru had been unlawfully killed, The Sunday Times reported last month.
It has prompted Labour to call on the government to investigate any possible "cover-up".
A defence source told the PA news agency: "The defence secretary has been impatient with the pace of this, and has directed full co-operation.
"He has worked with the military police and Kenyans to ensure their investigation is not impeded."