Police have named the eight-year-old boy who died after suffering "serious" injuries after being shot on a farm as Jay Cartmell.
The schoolboy from Frizington died on Saturday after being "seriously injured by a firearm" in the Warcop area of Cumbria.
A man in his 60s was arrested on suspicion of assault GBH at the scene.
He was later arrested on suspicion of gross negligence manslaughter, but released on bail.
Officers received "a report that a child had been seriously injured by a firearm" at 2.50pm on Saturday.
Jay was taken to hospital by air ambulance but died later.
Officers said the firearm was secured at the scene.
In an update on Monday, Cumbria Police said: "As officers continue with their enquiries into this incident, they are encouraging anyone who may have witnessed the incident or the moments leading up to it to come forward."
Responding to the tragic incident, Tim Farron, who is MP for the Westmorland and Lonsdale constituency, said: "This is an absolutely heartbreaking tragedy.
"I am praying for the family of the child and all those affected."
In a statement at the time, Cumbria Police said: "Police are investigating following the death of an eight-year-old boy.
"Emergency services were called at around 2.50pm yesterday (28 Sept) to a farm in the Warcop area following a report that a child had been seriously injured by a firearm at the property.
"Police and NWAS attended. The firearm was secured at the scene by police and an eight-year-old boy was taken to hospital by air ambulance having suffered serious and life-threatening injuries to his head and face.
"Sadly, the boy has died overnight.
"Officers arrested a man in his 60s at the scene on suspicion of assault GBH.
"He remains in police custody but is now under arrest on suspicion of gross negligence manslaughter."
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