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.
More top news
Heavy rain that has caused extensive flooding has left vehicles submerged and public transport severely disrupted in Aberdeen.
A slow start for most of us tomorrow with dribs and drabs of rain leaving some of us with a soggy journey into work.
The chief executive of one of the 'big six' energy companies tells ITV News a report customers are paying too much is a concern.