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
Firefighters across California have been battling major wildfires in what could be the most destructive wildfire season on record.
This summer's fundraising juggernaut, the ALS Ice Bucket challenge, has raised almost £7m in the fight against Motor Neurone Disease.
Winning entries from the Astronomy Photographer of the Year 2014 competition have been unveiled.