There has been a slight improvement in the condition of Darragh Somers, who was shot in the head in his school playground last week.
Darragh Somers "responded to his mother" in hospital
The five-year-old was awake for a time on Friday and responded to his mother. However, he remains critically ill.
Darragh was hit by a .22 bullet last Friday at a Fermanagh school. It is thought he was hit accidentally by someone shooting in nearby fields.
Police want anyone with information who has not yet come forward to do so.
Earlier this week, police urged the person who shot the child to consider contacting them through a clergyman.
Detective Chief Inspector Nigel Kyle said police were following a definite line of inquiry.
Police are understood to be examining 45 rifles as part of their investigation.
Ballistics experts are looking at legally held guns handed in by local people.
Police said they believed the shooting was an accident.
However, they said they may revise that theory if the person responsible did not come forward soon.
Police are investigating a report that someone was firing shots at a dog worrying sheep near the school.
They are also trying to trace a dark blue Toyota seen in the vicinity of the school at the time of the shooting.
They also want to locate a red pick-up truck which was seen near the school with a dead calf in the back, and a dark maroon coloured van.
Darragh is currently being treated in the Royal Belfast Hospital for Sick Children.