Imani Green may have been shot dead in revenge for an earlier attack.
The eight-year-old had been visiting relatives in Duncans - a town in northern Jamaica with a relatively low crime-rate - since shortly before the new year.
Police are investigating the theory, along with several other lines of inquiry.
The Foreign Office said it is providing consular assistance to Imani's family, from Balham, south London.
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Although a dull start can be expected, it will brighten up in eastern areas. Especially to the south.