Detective Superintendent Steve Brown of the Jamaican police has said he believes the shooting that resulted in the death of Imani Green was "targeted" but that she was not the target.
He said that police are still pursuing a number of leads but that they do not suspect gang involvement.
Imani Green's neighbours in Balham, south London, spoke today spoke of their sorrow following the eight-year-old girl's death in Jamaica.
A friend of the family, who asked not to be named, said: "This is a close-knit community, so this is going to hurt us."
Another added: "Nobody wants to speak, she was just a little girl. This is all so sad. We're distraught."
Neighbours said members of the girl's family took a flight to Jamaica early this morning to be with Imani's mother.
Speaking to ITV News, Imani's uncle Mitchum Brown described her as a "quiet, lovely, friendly girl" who had only just begun to grow in confidence.
Mr Brown explained how Imani had sickle cell anaemia as well as a hole in her heart, and how she would travel to Jamaica every winter with her family because the warm weather helped with her conditions.
He says Imani was an innocent victim of Friday's shooting and believes the gunman was taking revenge over a dispute with the cafe owner, who is Imani's cousin.
The sister of Imani Green said she found the eight-year-old in a pool of blood after a lone gunman shot her twice in front of relatives in a cafe in Jamaica on Friday.
Janella Palmer, 19, told the BBC her sister was still breathing when she reached her.
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.
The eight-year-old British girl killed in front of relatives in a shop in the town of Duncans inTrelawny, northern Jamaica, was shot in the head and shoulder by a lone gunman, local Radio station RJR News reported.
Imani suffered from the blood disorder sickle cell aneamia and was in the country to cope with the disease, the youngster's brother told Sky News. She died while undergoing treatment at a local hospital.
Three other people were injured during the shooting and remain in a stable condition in a local hospital.
Police in Jamaica have confirmed that an eight-year-old girl from London has been shot dead while visiting family in the country.
Imani Green was in a shop in the rural north coast town of Duncans when a man opened fire at a group of people inside, Jamaican Deputy Superintendent of Police Steve Brown said.
Imani was taken to hospital and later died.
He added that the police are continuing with their enquiries.
An eight-year-old girl from London has been shot dead while visiting family in Jamaica, according to local media reports.
She was reportedly shot after an argument broke out at a store in the north coast area of Duncans and a man then opened fire.
A Foreign Office spokesperson said, "We can confirm the death of a British national in Jamaica on the 11th January. We are providing consular assistance and liaising with local authorities".